SAKAI Takashi 酒井隆

… Alternative Names

酒井隆サカイタカシ

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Researcher Number	70005809
Other IDs
External Links
Affiliation (based on the past Project Information) *help	2009: 岡山理科大学, 理学部, 教授 2005 – 2007: Okayama Univ.Sci., Fac.Sci., Prof., 理学部, 教授 1993 – 2004: 岡山大学, 理学部, 教授 2001: Okayama University, Faculty of Science, Professor, 理学部, 教授 1988 – 1991: 岡山大学, 理学部, 教授 1986: 岡山大, 理学部, 教授
Review Section/Research Field	Principal Investigator Geometry / 代数学・幾何学 / Geometry Except Principal Investigator Geometry / Geometry / 代数学・幾何学 / Global analysis / Global analysis / 解析学
Keywords	Principal Investigator リーマン多様体 / 曲率 / 測地線 / Riemannian manifolds / Distance functions / 距離関数 / 比較定理 / 位相構造 / Cut loci / Geodesics … More / Morse theory / 切断跡 / モース理論 / Metric Invariants / Curvatures / Alexandrov spaces / 計量不変量 / アレキサンドロフ空間 / Warped product / Comparison Theorem / Geodesic / Curvature / 捩れ積 / ねじれ積 / Curvature and Topology / Manifold Structures / Geometric Structure / 曲率と位相 / 多様体構造 / 幾何構造 / グロモフの収来定理 / 単射半径 / リ-マン幾何学 / 比較定理とその応用 / 幾何学不等式 / 計量構造 … More Except Principal Investigator スペクトル / 逆問題 / 安定性 / 多様体 / Liouville manifold / リーマン多様体 / inverse problem / ラプラシアン / スペクトル逆問題 / 測地線 / Integrable geodesic flow / cut locus / 可積分測地流 / リウヴィル多様体 / 共役跡 / カットローカス / 楕円体 / 半古典近似 / 酔歩 / graph / グラフ / P-調和写像 / Laplacian / stability / spectrum / manifold / 等質空間 / 極小曲面 / 距離関数 / K理論 / コホモロジー / Lie contact structure / minimal surfaces / homogeneous spaces / Yang-Mills connection / curvature / Einstein metric / 部分多様体 / ラプラスベルトラミ作用素 / 対称空間 / リ-マン多様体 / リッテ曲率 / 熱方程式 / 調和写像 / 力学系 / 複素多様体 / リ-接触構造 / リー接触構造 / ヤングミルズ接続 / 曲率 / アインシュタイン計量 / Hermite-Liouville / Kahler-Liouville / Cusp / Conjugate locus / Cut locus / Ellipsoid / エルミート・リウヴィル多様化 / ケーラー・リウヴィル多様体 / カスプ / 可積化測地流 / unfolding of polyhedron / farthest point / distance function / guadric surface / 1'st conjugate locus / geodesies / モース理論 / Liouville曲面 / 多面体の展閲 / 単純閉擬測地線 / Liouvolle曲面 / 多面体の展開 / 最遠点 / 二次曲面 / Liouville多様体 / 第1共役跡 / 最小跡 / Riemannian manifold / p-harmonic map / p-harmonic function / p-harmonic morphism / p-ラプラシアン / 幾何学 / p-調和関数 / p-調和写像 / quadratic surface / tri-axial ellipsoid / Jacobi / conjugate locus / ellipsoid / 双曲面 / 射影同値 / 極 / リウヴィル曲面 / 共役蹠 / 2次曲面 / 楕円面 / ヤコビ / boundary distance / 双曲力学系 / 境界距離 / spectre / nilpotent / heat kernel / random walk / べき零 / 熱核 / Gromov-Hausdorff convergence / Inverse spectral Problem / nilpotent groups / random walks / ハーパー作用素 / ハイゼンベルグ群 / グロモフハウスドルフ収束 / べき零群 / ランダムウォーク / P-Laplace operator / P-harmonic map / スペクトラム / 第1固有値 / P-ラプラシアン / P-harmonic morphism / グリーン核 / 無限グラフ / P-ラプラス作用素 / Aharonov-Bohm effect / scattering by magnetic field / point interaction / resolvent convergence / scattering at low energy / magnetic Schrodinger operator / 散乱振幅 / アハロノフ・ボウム効果 / 磁場散乱 / スペクトル理論 / シュレディンガー作用素 / アハラノフ・ボーム効果 / 磁場による散乱 / デルタ型磁場 / レゾルベント収束 / 磁場をもつシュレディンガー作用素 / isoperimetric constants / isospectral graphs / the Hausdorff distance / 等周定数 / 等スペクトルグラフ / ハウスドルフ距離 / Differential Geometry / Floerホモロジー / 幾何学的変分問題 / シンプレクテイック幾何学 / リーマン幾何学 / 微分幾何学 / 双曲型 / 局所等質空間 / 作用 / 位相的性質 / 微分幾何学的量 / 等長変換群 / 等周不等式 / 閉測地線 / ホモトピー型 / A(p)構造 / 作用素 / 同境理論 / ヒルベルト変換 / フーリエ変換 / タウバー型定理 / 調和解析 / 密度 / Benfordの規則 / 指数和 / グロモフ-ハウスドルフ距離 / スペクトル収束 / グラフのラプラシアン / 一般ホモロジー理論 / コンフィグレーション空間 / 分類空間 / 同変ホモトピー論 / エルゴード定理 / 線形作用素 / リーマン計量 / 変換群 / 根基 / 自己入射的 / 局所有限環 / 有限環 / 多項式関係 / 周期環 / 強正則環 / 強π正則環 / 局所化空間 / Hubbuck作用素 / アダムス作用素 / H空間の結合性 / 可換性定理 / 強固有環 / 面積と直径に関する不等式 / リ-マン計量 Less

Geometric Structures and Topology
- Principal Investigator
  
  KATSUDA Atsushi
- Project Period (FY)
  2007 – 2009
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Geometry
- Research Institution
  Okayama University
Problems related to integrable geodesic flows
- Principal Investigator
  
  KIYOHARA Kazuyoshi
- Project Period (FY)
  2006 – 2007
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Geometry
- Research Institution
  Okayama University
Metric invariants and space structuresPrincipal Investigator
- Principal Investigator
  
  SAKAI Takashi
- Project Period (FY)
  2005 – 2007
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Geometry
- Research Institution
  Okayama University of Science
Comprehensive studies of cut locus
- Principal Investigator
  
  ITOH Jin-ichi
- Project Period (FY)
  2005 – 2007
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Geometry
- Research Institution
  Kumamoto University
Relations of geometric structure of manifolds and graphs, spectre, asymptotic analysis and their applications
- Principal Investigator
  
  KATSUDA Atsushi
- Project Period (FY)
  2004 – 2006
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Geometry
- Research Institution
  OKAYAMA UNIVERSITY
Integrable geodesic flows and related problems
- Principal Investigator
  
  KIYOHARA Kazuyoshi
- Project Period (FY)
  2004 – 2005
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Geometry
- Research Institution
  Okayama University
studies on the relationship of the structure of manifolds and p-harmonic functions
- Principal Investigator
  
  TAKEUCHI Hiroshi
- Project Period (FY)
  2004 – 2007
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Global analysis
- Research Institution
  Shikoku University
Spectra and Geometric structure of manifolds and graph
- Principal Investigator
  
  KATSUDA Atsushi
- Project Period (FY)
  2002 – 2003
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Geometry
- Research Institution
  OKAYAMA UNIVERSITY
Relations between space-structures and curvaturesPrincipal Investigator
- Principal Investigator
  
  SAKAI Takashi
- Project Period (FY)
  2000 – 2003
- Research Category
  
  Grant-in-Aid for Scientific Research (B)
- Research Field
  
  Geometry
- Research Institution
  OKAYAMA UNIVERSITY
Geometric Structures on Manifolds and Graphs
- Principal Investigator
  
  KATSUDA Atsushi
- Project Period (FY)
  2000 – 2001
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Geometry
- Research Institution
  OKAYAMA UNIVERSITY
Spectral Theory for Schrodinger Operators with Magnetic Fields and its Application
- Principal Investigator
  
  TAMURA Hideo
- Project Period (FY)
  1999 – 2000
- Research Category
  
  Grant-in-Aid for Scientific Research (B).
- Research Field
  
  Global analysis
- Research Institution
  Okayama University
The properties of P-harmonic maps and the application to Geometry
- Principal Investigator
  
  TAKEUCHI Hiroshi
- Project Period (FY)
  1999 – 2001
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Global analysis
- Research Institution
  Shikoku University
Geometric structure and topology of manifolds and graphs
- Principal Investigator
  
  KATSUDA Atsushi
- Project Period (FY)
  1998 – 1999
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Geometry
- Research Institution
  Okayama University
CURVATURE AND STRUCURE OF SPACESPrincipal Investigator
- Principal Investigator
  
  SAKAI Takashi
- Project Period (FY)
  1997 – 1998
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Geometry
- Research Institution
  OKAYAMA UNIVERSITY
計量構造と多様体構造Principal Investigator
- Principal Investigator
  
  酒井隆
- Project Period (FY)
  1996
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Geometry
- Research Institution
  Okayama University
多様体の幾何構造と位相
- Principal Investigator
  
  勝田篤
- Project Period (FY)
  1996
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Geometry
- Research Institution
  Okayama University
幾何構造と位相構造Principal Investigator
- Principal Investigator
  
  酒井隆
- Project Period (FY)
  1995
- Research Category
  
  Grant-in-Aid for General Scientific Research (C)
- Research Field
  
  Geometry
- Research Institution
  Okayama University
Differential Geometric Reserch on Manifolds
- Principal Investigator
  
  KENMOTSU Katsuei
- Project Period (FY)
  1995 – 1996
- Research Category
  
  Grant-in-Aid for Scientific Research (A)
- Research Field
  
  Geometry
- Research Institution
  Tohoku University
同変ホモトピー論とその応用
- Principal Investigator
  
  島川和久
- Project Period (FY)
  1994
- Research Category
  
  Grant-in-Aid for General Scientific Research (C)
- Research Field
  
  Geometry
- Research Institution
  Okayama University
多様体とコホモロジー論
- Principal Investigator
  
  SHIMAKAWA Kazuhisa
- Project Period (FY)
  1993
- Research Category
  
  Grant-in-Aid for General Scientific Research (C)
- Research Field
  
  Geometry
- Research Institution
  Okayama University
環と加群の構造
- Principal Investigator
  
  平野康之
- Project Period (FY)
  1991
- Research Category
  
  Grant-in-Aid for General Scientific Research (C)
- Research Field
  
  代数学・幾何学
- Research Institution
  Okayama University
計量構造と位相構造Principal Investigator
- Principal Investigator
  
  酒井隆
- Project Period (FY)
  1990
- Research Category
  
  Grant-in-Aid for General Scientific Research (C)
- Research Field
  
  代数学・幾何学
- Research Institution
  Okayama University
一般コホモロジ-論
- Principal Investigator
  
  藤井道一
- Project Period (FY)
  1989
- Research Category
  
  Grant-in-Aid for General Scientific Research (C)
- Research Field
  
  代数学・幾何学
- Research Institution
  Okayama University
Geometric Structures and Manifold StructuresPrincipal Investigator
- Principal Investigator
  
  SAKAI Takashi
- Project Period (FY)
  1989 – 1990
- Research Category
  
  Grant-in-Aid for Co-operative Research (A)
- Research Field
  
  代数学・幾何学
- Research Institution
  Okayama University
一般コホモロジー論
- Principal Investigator
  
  藤井道一
- Project Period (FY)
  1988
- Research Category
  
  Grant-in-Aid for General Scientific Research (C)
- Research Field
  
  代数学・幾何学
- Research Institution
  Okayama University
可微分多様体の大域的構造について
- Principal Investigator
  
  SHIOHAMA Katsuhiro
- Project Period (FY)
  1988 – 1990
- Research Category
  
  Grant-in-Aid for Co-operative Research (A)
- Research Field
  
  代数学・幾何学
- Research Institution
  Kyushu University
指数和の評価とその応用
- Principal Investigator
  
  鹿野健
- Project Period (FY)
  1987 – 1988
- Research Category
  
  Grant-in-Aid for General Scientific Research (C)
- Research Field
  
  解析学
- Research Institution
  Okayama University
計量構造と位相構造Principal Investigator
- Principal Investigator
  
  酒井隆
- Project Period (FY)
  1986
- Research Category
  
  Grant-in-Aid for General Scientific Research (C)
- Research Field
  
  代数学・幾何学
- Research Institution
  Okayama University

All 2008 2007 2006 2005 Other

All Journal Article Presentation Book

[Book] EOLSS Encyclopedia of life support system), 6.1.3.4, Differential Geometry2008
- Author(s)
  T. Sakai
- Publisher
  Unesco Web(発行予定)
- Data Source
  KAKENHI-PROJECT-17540079
[Book] 解決!ポアンカレ予想(数学セミナー増刊)2007
- Author(s)
  小島定吉, 糸川銚, 酒井隆, 戸田正人, 小林治, 二木昭人, 浦川肇, 十文字正樹, 山口孝男, 塩谷隆, 小林亮一
- Total Pages
  94
- Publisher
  日本評論社
- Data Source
  KAKENHI-PROJECT-17540079
[Book] 現代幾何学の流れ(砂田利一編):ベルジェ/幾何のエスプリ2007
- Author(s)
  酒井隆(共著)
- Publisher
  日本評論社
- Description
  「研究成果報告書概要(和文)」より
- Data Source
  KAKENHI-PROJECT-17540079
[Book] 解決ボアンカレ予想(数学セミナー増刊号);曲率を調べると位相がわかる2007
- Author(s)
  酒井隆(共著)
- Publisher
  日本評論社
- Description
  「研究成果報告書概要(和文)」より
- Data Source
  KAKENHI-PROJECT-17540079
[Book] EOLSS(Encyclopedia of life support system), 6.1.3.4, Differential Geometry
- Author(s)
  T.Sakai
- Publisher
  Unesco(Web 上発行確定)
- Description
  「研究成果報告書概要(和文)」より
- Data Source
  KAKENHI-PROJECT-17540079
[Book] EOLSS(Encyclopedia of life support system), 6. 1. 3. 4, Differential Geometry
- Author(s)
  T. Sakai
- Total Pages
  21
- Publisher
  Unesco(in a web encyclopedia)(to appear)
- Description
  「研究成果報告書概要(欧文)」より
- Data Source
  KAKENHI-PROJECT-17540079
[Journal Article] Cut loci and distance functions2007
- Author(s)
  J.Itoh, T.Sakai
- Journal Title
  
  Math.J.Okayama Univ. 19
  
  Pages: 65-92
- NAID
  120002309399
- Description
  「研究成果報告書概要(和文)」より
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-17540079
[Journal Article] Cut loci and distance functions2007
- Author(s)
  J. Itoh, T. Sakai
- Journal Title
  
  Math.J.Okayama Univ 49
  
  Pages: 65-92
- NAID
  120002309399
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-17540079
[Journal Article] One can see the topology looking at the curvature2007
- Author(s)
  T. Sakai(coauthor)
- Journal Title
  
  Solution of the Poincare Conjecture(Special Issue of SugakwSeminar). Nippon-Hyoron-Sha
- Description
  「研究成果報告書概要(欧文)」より
- Data Source
  KAKENHI-PROJECT-17540079
[Journal Article] 書評:M.Berger;A Panoramic View of Riemannian Geometry,Springer,2003年,XXIII+824ページ2007
- Author(s)
  酒井隆
- Journal Title
  
  数学 59
  
  Pages: 216-221
- Description
  「研究成果報告書概要(和文)」より
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-17540079
[Journal Article] Cut loci and distance functions2007
- Author(s)
  J.Itoh, T.Sakai
- Journal Title
  
  Mathematical Journal of Okayama Univ. 49(To appear)
- NAID
  120002309399
- Data Source
  KAKENHI-PROJECT-17540079
[Journal Article] Cut loci and distance functions2007
- Author(s)
  J. Itoh, T. Sakai
- Journal Title
  
  Math. J. Okayama Univ. 49
  
  Pages: 65-92
- NAID
  120002309399
- Description
  「研究成果報告書概要(欧文)」より
- Data Source
  KAKENHI-PROJECT-16540208
[Journal Article] Bergen Esprit of Geometry2007
- Author(s)
  T. Sakai(coauthor)
- Journal Title
  
  Currents of Modern Geometry (ed., T. Sunada). Nippon- Hyoron-Sha
- Description
  「研究成果報告書概要(欧文)」より
- Data Source
  KAKENHI-PROJECT-17540079
[Journal Article] 書評:M. Berger : A panoramic View of Riemannian Geometry, Springer, 2003年, XXIII+824ページ2007
- Author(s)
  酒井隆
- Journal Title
  
  数学 59巻2号
  
  Pages: 216-221
- Data Source
  KAKENHI-PROJECT-17540079
[Journal Article] Cut loci and distance functions2007
- Author(s)
  J., Itoh, T., Sakai
- Journal Title
  
  Math. J. of Okayama Univ. 49
  
  Pages: 65-92
- NAID
  120002309399
- Description
  「研究成果報告書概要(欧文)」より
- Data Source
  KAKENHI-PROJECT-17540085
[Journal Article] Book Review : M. Berger ; A Panoramic View of Riemannian Geometry Springer, 2003, XXIII + 824(in Japanese)2007
- Author(s)
  T. Sakai
- Journal Title
  
  Sugaku 59-2
  
  Pages: 216-221
- Description
  「研究成果報告書概要(欧文)」より
- Data Source
  KAKENHI-PROJECT-17540079
[Journal Article] 書言平:M.Berger;A Panoramic View of Riemannian Geometry,Springer,2003年,XXIII+824ページ2007
- Author(s)
  酒井隆
- Journal Title
  
  数学 59
  
  Pages: 216-221
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-17540079
[Journal Article] Cut loci and distance functions2007
- Author(s)
  J. Itoh, T. Sakai
- Journal Title
  
  Math.J.of Okayama Univ. 49
  
  Pages: 65-92
- NAID
  120002309399
- Description
  「研究成果報告書概要(和文)」より
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-17540085
[Journal Article] Cut loci and distance functions2007
- Author(s)
  J.Itoh, T.Sakai
- Journal Title
  
  Math.J.Okayama Univ. 49
  
  Pages: 65-92
- NAID
  120002309399
- Description
  「研究成果報告書概要(和文)」より
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-16540208
[Journal Article] Cut loci and distance functions2007
- Author(s)
  J. Itoh, T. Sakai.
- Journal Title
  
  Math. J. Okayama Univ. 49
  
  Pages: 65-92
- NAID
  120002309399
- Description
  「研究成果報告書概要(欧文)」より
- Data Source
  KAKENHI-PROJECT-17540079
[Journal Article] Cut loci and distance functions2007
- Author(s)
  J. Itoh. T. Sakai
- Journal Title
  
  Math. J. Okayama Univ. 49
  
  Pages: 65-92
- NAID
  120002309399
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-19540088
[Journal Article] Cut loci and distance functions2007
- Author(s)
  J.Itoh & T.Sakai
- Journal Title
  
  Math.J.of Okayama Univ. 49
  
  Pages: 65-92
- NAID
  120002309399
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-17540085
[Journal Article] Lines and geometry-what is straight and what is curved(in Japanese)2006
- Author(s)
  T. Sakai
- Journal Title
  
  Sugaku Tsusin 10-4
  
  Pages: 5-23
- Description
  「研究成果報告書概要(欧文)」より
- Data Source
  KAKENHI-PROJECT-17540079
[Journal Article] "直線"と幾何学-真っ直ぐなものと曲がったもの-2006
- Author(s)
  酒井隆
- Journal Title
  
  数学通信(日本数学会) 10・4
  
  Pages: 5-23
- Data Source
  KAKENHI-PROJECT-17540079
[Journal Article] 直線と幾何学-真っ直ぐなものと曲がったもの-2006
- Author(s)
  酒井隆
- Journal Title
  
  数学通信 10
  
  Pages: 5-23
- Description
  「研究成果報告書概要(和文)」より
- Data Source
  KAKENHI-PROJECT-17540079
[Journal Article] Curvature-up through the twentieth century,and its future2005
- Author(s)
  T. Sakai
- Journal Title
  
  Sugaku Expositions 18
  
  Pages: 165-187
- Description
  「研究成果報告書概要(和文)」より
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-17540085
[Journal Article] Curvature-up through the twentieth century, and its future?2005
- Author(s)
  T., Sakai
- Journal Title
  
  Sugaku Expositions 18
  
  Pages: 165-187
- Description
  「研究成果報告書概要(欧文)」より
- Data Source
  KAKENHI-PROJECT-17540085
[Journal Article] Curvature-up through the twentieth century,and its future2005
- Author(s)
  T.Sakai
- Journal Title
  
  Sugaku Expositions 18
  
  Pages: 165-187
- Description
  「研究成果報告書概要(和文)」より
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-17540079
[Journal Article] Curvature-up through the twentieth century, and the future?2005
- Author(s)
  T. Sakai
- Journal Title
  
  Sugaku Expositions 18-2
  
  Pages: 165-187
- Description
  「研究成果報告書概要(欧文)」より
- Data Source
  KAKENHI-PROJECT-17540079
[Journal Article] Cut loci and distance functions
- Author(s)
  Itoh, J., Sakai, T.
- Journal Title
  
  Math. J.of Okayama Univ.(受理)
- NAID
  120002309399
- Data Source
  KAKENHI-PROJECT-17540085
[Presentation] 種数2の閉曲面に対する等縮不等式2007
- Author(s)
  酒井隆
- Organizer
  福岡微分幾何学研究集会
- Place of Presentation
  福岡大学セミナーハウス
- Year and Date
  2007-02-01
- Description
  「研究成果報告書概要(和文)」より
- Data Source
  KAKENHI-PROJECT-17540079
[Presentation] Isosystolic inequality for surface of genus 22007
- Author(s)
  T. Sakai
- Organizer
  Fukuoka Seminar on Differential Geometry
- Place of Presentation
  Fukuoka Univ. Seminar House
- Year and Date
  2007-02-01
- Description
  「研究成果報告書概要(欧文)」より
- Data Source
  KAKENHI-PROJECT-17540079
[Presentation] Morse theory of distance functions and cut loci2005
- Author(s)
  T. Sakai
- Organizer
  Differential Equations on Manifolds
- Place of Presentation
  Satelite Plaza of Kanazawa Univ
- Year and Date
  2005-12-12
- Description
  「研究成果報告書概要(欧文)」より
- Data Source
  KAKENHI-PROJECT-17540079
[Presentation] 直線と幾何学-真っ直ぐなものと曲がったもの-2005
- Author(s)
  酒井隆
- Organizer
  2005年秋の日本数学会市民講演会
- Place of Presentation
  岡山大学
- Year and Date
  2005-09-18
- Description
  「研究成果報告書概要(和文)」より
- Data Source
  KAKENHI-PROJECT-17540079
[Presentation] Morse theory of distance functions2005
- Author(s)
  T. Sakai
- Organizer
  Okayama Colloquium on Geometry
- Place of Presentation
  Okayama University of Science
- Year and Date
  2005-06-24
- Description
  「研究成果報告書概要(欧文)」より
- Data Source
  KAKENHI-PROJECT-17540079
[Presentation] Lines and geometry-what is straight and what is curved2005
- Author(s)
  T. Sakai
- Organizer
  Math. Soc. of Japan Lecture for Citizens
- Place of Presentation
  Okayama Univ
- Year and Date
  2005-09-18
- Description
  「研究成果報告書概要(欧文)」より
- Data Source
  KAKENHI-PROJECT-17540079
[Presentation] 距離関数のMorse理論とcut locus2005
- Author(s)
  酒井隆
- Organizer
  研究集会「多様体上の微分方程式」
- Place of Presentation
  金沢大学サテライト・プラザ講義室
- Year and Date
  2005-12-12
- Description
  「研究成果報告書概要(和文)」より
- Data Source
  KAKENHI-PROJECT-17540079
[Presentation] 距離関数のモース理論2005
- Author(s)
  酒井隆
- Organizer
  第3回岡山幾何学談話会
- Place of Presentation
  岡山理科大学
- Year and Date
  2005-06-24
- Description
  「研究成果報告書概要(和文)」より
- Data Source
  KAKENHI-PROJECT-17540079

1. KATSUDA Atsushi (60183779)

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2. SHIMAKAWA Kazuhisa (70109081)

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SAKAI Takashi 酒井 隆

酒井 隆 サカイ タカシ

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Metric invariants and space structuresPrincipal Investigator

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Relations between space-structures and curvaturesPrincipal Investigator

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CURVATURE AND STRUCURE OF SPACESPrincipal Investigator

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計量構造と多様体構造Principal Investigator

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SAKAI Takashi 酒井隆

酒井隆サカイタカシ