2001 年度実績報告書

微分式系と部分多様体論

研究課題

研究課題/領域番号	12640087
研究機関	上智大学
研究代表者	宮岡礼子上智大学, 理工学部, 教授 (70108182)
研究分担者	加藤昌英上智大学, 理工学部, 教授 (90062679) 内山康一上智大学, 理工学部, 教授 (20053689) 田丸博士上智大学, 理工学部, 助手 (50306982) 梅原雅顕広島大学, 大学院・理学研究科, 教授 (90193945) 横山和夫上智大学, 理工学部, 助教授 (10053711)
キーワード	ガウス写像 / ラグランジアン部分多様体 / Austere部分多様体 / 等径超曲面 / 型作用素 / 可積分系 / 平均曲率一定曲面 / 調和写像
研究概要	等径超曲面の主曲率が6個の分類にとりくみ,重複度1のときの等質性の新しい幾何学的証明を与えた.関連して,ガウス写像の退化する部分多様体の研究をし,分担者の石川剛郎氏と木村真琴氏とともに多くの新しい例を与えた.等径超曲面のすべての焦部分多様体と,ガウス写像の退化する等径超曲面はAustere部分多様体で,その法束からスペシャルラグランジアン部分多様体が構成できる.これは体積最小だが,完備プロパーなR^nのAustere部分多様体は半分次元以下の次元のCW複体のホモトピー型を持つことを証明でき,その法束の体積最小性との関連が大変興味深い.さらに分担者,芥川(相山)玲子,梅原雅章らとは,2つの調和写像から球面の平均曲率一定曲面を大域的に得るための必要十分条件を得て,応用として,トーラスからの等長だが合同でない平均曲率一定曲面を構成することを研究中である. 田丸はある非コンパクト型対称空間のイソトロピー軌道を分類した.内山は非線形常微分方程式の特異点を調べた.横山は拡張DSダイヤグラムの理論を完成した.相山は空間型の曲面,C^2のラグランジアン曲面などに対する多くの表現項式を与えた.石川剛郎は,空間曲線の可展面の位相的分類を与えたほか,接触多様体の特異点を調べた.宇田川はトーラスからグラスマン多様体への調和写像を詳しく調べ,楕円関数で記述した.またエルミート対称空間内の円の研究をした.梅原は,曲線の特異点,極小曲面のエンドの研究,そのガウス写像に関連した一定曲率1を持つ曲面の内在的研究をした.木村真琴は,部分多様体上の円周束,さらに球面束の等質埋め込みの例をたくさん考えた.

研究成果

(33件)

すべてその他

すべて文献書誌 (33件)

[文献書誌] R. Aiyama: "A global correspondence between CMC-surfaces in S^3 and pairs of non-conformal harmonic maps into S^2"Proc. Amer. Math. Soc.. 128. 939-941 (2000)
[文献書誌] R. Miyaoka: "A simple proof of the homogeneity of isoparametric hypersurfaces with (g, m) = (6, 1)"Geometry and Topology of Submanifolds X. 178-199 (2000)
[文献書誌] G. Ishikawa: "Submanifolds with degenerate Gauss mappings in the spheres"Josai Mathematical Monograph. Differential Geometry. 3. 125-138 (2001)
[文献書誌] S. Kaneyuki: "Compactification of parahermitian symmetric spaces and its applicationsI : Tube-type realizations"Proceedings of the III International Workshop : Lie Theory and Its Applications in Physics, World Scientific. 63-74 (2000)
[文献書誌] K. Balachandran: "Existence of solutions of nonlinear integrodifferential equations of Sobolev type with nonlocal condition in Banach spaces"Proc. Indian Acad. Sci. (Math. Sci.). 110, No.2. 225-232 (2000)
[文献書誌] K. Balachandran: "Existence of solutions of quasilinear integrodifferential equations with nonlocal condition"Tokyo J. Math.. 23.No1. 203-210 (2000)
[文献書誌] H. Ikeda: "Remodeling a DS-diagram into one with E-cycle"Tokyo Jour. Math.. 23. 113-135 (2000)
[文献書誌] R. Aiyama: "Kenmotsu type respresentation formula for surfaces with prescribed mean curvature in the 3-sphere"Tohoku Math. J.. 52. 95-105 (2000)
[文献書誌] R. Aiyama: "Kenmotsu type representation formula for spacelike surfaces with prescribed mean in the de Sitter 3-space"Tsukuba J. Math.. 24. 189-196 (2000)
[文献書誌] R. Aiyama: "Minimal maps between the hyperbolic disc and generalized Gauss maps of maximal surfaces in the anti-de Sitter 3-space"Tohoku Math. J.. 52. 415-429 (2000)
[文献書誌] R. Aiyama: "Kenmotsu type representation formula for surfaces with prescribed mean curvature in the hyperbolic 3-space"J. Math. Soc. Japan. 52. 877-898 (2000)
[文献書誌] R. Aiyama: "Totally real surfaces in the complex 2-space : Steps in Differential Geometry"Proceedings of the Colloquium on Differential Geometry. July. 25-30 (2000)
[文献書誌] R. Aiyama: "Lagrangian surfaces in the complex 2-space"Proceedings of the 5th International Workshop(Kyungpooh U.). 25-29 (2001)
[文献書誌] R. Aiyama: "Constant mean curvature surfaces in the hyperbolic 3-space and harmonic maps"Proceedings of the 5th International Workshop(Kyungpooh U.). 31-39 (2001)
[文献書誌] G. Ishikawa: "Topological classification of the tangent developables of space curves"Journal of London Math. Soc.. 62-2. 583-598 (2000)
[文献書誌] G. Ishikawa: "Solution surfaces of the Monge-Ampere equation"Differential Geometry and its Applications. 14. 113-124 (2001)
[文献書誌] M. Kimura: "Minimal immersions of some circle bundles over holomorphic curves in complex quadric to sphere"Osaka Math. J.. 37. 883-903 (2000)
[文献書誌] U-Hang Ki: "Geometry of holomorphic distributions of real hypersurfaces in a complexprojective space"Czec. Math. J.. 51. 197-204 (2001)
[文献書誌] T. Adachi: "Simpleness and closedness of circles in compact Hermitian symmetricspaces"Tsukuba J. Math.. 24 No1. 1-13 (2000)
[文献書誌] S. Kato: "General existence of minimal : surfaces of genus zero with catenoidal ends and prescribed flux"Communications in Analysis and Geometry. 8. 83-114 (2000)
[文献書誌] M. Umehara: "Metrics of constant curvature 1 with three conical singularities on the 2-sphere"Illinois Journal of Mathematics. 44 No1. 72-94 (2000)
[文献書誌] A. I. Bobenko: "Monodromy of isometric deformation of CMC surfaces"Hiroshima Mathematical Journal. 31. 291-297 (2001)
[文献書誌] 宮岡礼子: "Lie sphere geometry and Lie contact structure"数理解析研究所講究録. 1150. 143-146 (2000)
[文献書誌] 宮岡礼子: "Elie Cartanの業績-S. S. ChernとC. Chevaleyによる解説"数理解析研究所講究録. 1206. 1-31 (2001)
[文献書誌] 宮岡礼子: "等径超曲面今昔-Elie Cartanと21世紀"数理解析研究所講究録. 1206. 32-44 (2001)
[文献書誌] 宮岡礼子: "On special Lagragian submanifolds"数理解析研究所講究録. 1236. 1-8 (2001)
[文献書誌] 宮岡礼子: "等径超曲面再訪"数学. 53. 18-33 (2001)
[文献書誌] 梅原雅顕: "3次元双曲型空間における平坦な曲面"数理解析研究所講究録. 1236. 49-59 (2001)
[文献書誌] 金行壯二: "Recent Development in Geometry of Parahermitian Symmetric spaces"数理解析研究所講究録. 1150. 11-13 (2000)
[文献書誌] 相山玲子: "A construction of Lagrangian surfaces in the complex 2-space"数理解析研究所講究録. 1206. 121-133 (2001)
[文献書誌] 石川剛郎: "Recent Results on Developable Submanifolds : Examples and Classifications"数理解析研究所講究録. 1150. 134-141 (2000)
[文献書誌] J. Faraut: "Analysis And Geometry On Complex Homogeneous Domains Progress in Math vol.185"Birkhauser. (2000)
[文献書誌] 石川剛郎: "代数曲線と特異点, 特異点の数理. 第4巻"共立出版. (2001)

2001 年度 実績報告書

微分式系と部分多様体論

研究代表者

宮岡 礼子 上智大学, 理工学部, 教授 (70108182)

研究成果

[文献書誌] R. Aiyama: "A global correspondence between CMC-surfaces in S^3 and pairs of non-conformal harmonic maps into S^2"Proc. Amer. Math. Soc.. 128. 939-941 (2000)

[文献書誌] R. Miyaoka: "A simple proof of the homogeneity of isoparametric hypersurfaces with (g, m) = (6, 1)"Geometry and Topology of Submanifolds X. 178-199 (2000)

[文献書誌] G. Ishikawa: "Submanifolds with degenerate Gauss mappings in the spheres"Josai Mathematical Monograph. Differential Geometry. 3. 125-138 (2001)

[文献書誌] S. Kaneyuki: "Compactification of parahermitian symmetric spaces and its applicationsI : Tube-type realizations"Proceedings of the III International Workshop : Lie Theory and Its Applications in Physics, World Scientific. 63-74 (2000)

[文献書誌] K. Balachandran: "Existence of solutions of nonlinear integrodifferential equations of Sobolev type with nonlocal condition in Banach spaces"Proc. Indian Acad. Sci. (Math. Sci.). 110, No.2. 225-232 (2000)

[文献書誌] K. Balachandran: "Existence of solutions of quasilinear integrodifferential equations with nonlocal condition"Tokyo J. Math.. 23.No1. 203-210 (2000)

[文献書誌] H. Ikeda: "Remodeling a DS-diagram into one with E-cycle"Tokyo Jour. Math.. 23. 113-135 (2000)

[文献書誌] R. Aiyama: "Kenmotsu type respresentation formula for surfaces with prescribed mean curvature in the 3-sphere"Tohoku Math. J.. 52. 95-105 (2000)

[文献書誌] R. Aiyama: "Kenmotsu type representation formula for spacelike surfaces with prescribed mean in the de Sitter 3-space"Tsukuba J. Math.. 24. 189-196 (2000)

[文献書誌] R. Aiyama: "Minimal maps between the hyperbolic disc and generalized Gauss maps of maximal surfaces in the anti-de Sitter 3-space"Tohoku Math. J.. 52. 415-429 (2000)

[文献書誌] R. Aiyama: "Kenmotsu type representation formula for surfaces with prescribed mean curvature in the hyperbolic 3-space"J. Math. Soc. Japan. 52. 877-898 (2000)

[文献書誌] R. Aiyama: "Totally real surfaces in the complex 2-space : Steps in Differential Geometry"Proceedings of the Colloquium on Differential Geometry. July. 25-30 (2000)

[文献書誌] R. Aiyama: "Lagrangian surfaces in the complex 2-space"Proceedings of the 5th International Workshop(Kyungpooh U.). 25-29 (2001)

[文献書誌] R. Aiyama: "Constant mean curvature surfaces in the hyperbolic 3-space and harmonic maps"Proceedings of the 5th International Workshop(Kyungpooh U.). 31-39 (2001)

[文献書誌] G. Ishikawa: "Topological classification of the tangent developables of space curves"Journal of London Math. Soc.. 62-2. 583-598 (2000)

[文献書誌] G. Ishikawa: "Solution surfaces of the Monge-Ampere equation"Differential Geometry and its Applications. 14. 113-124 (2001)

[文献書誌] M. Kimura: "Minimal immersions of some circle bundles over holomorphic curves in complex quadric to sphere"Osaka Math. J.. 37. 883-903 (2000)

[文献書誌] U-Hang Ki: "Geometry of holomorphic distributions of real hypersurfaces in a complexprojective space"Czec. Math. J.. 51. 197-204 (2001)

[文献書誌] T. Adachi: "Simpleness and closedness of circles in compact Hermitian symmetricspaces"Tsukuba J. Math.. 24 No1. 1-13 (2000)

[文献書誌] S. Kato: "General existence of minimal : surfaces of genus zero with catenoidal ends and prescribed flux"Communications in Analysis and Geometry. 8. 83-114 (2000)

[文献書誌] M. Umehara: "Metrics of constant curvature 1 with three conical singularities on the 2-sphere"Illinois Journal of Mathematics. 44 No1. 72-94 (2000)

[文献書誌] A. I. Bobenko: "Monodromy of isometric deformation of CMC surfaces"Hiroshima Mathematical Journal. 31. 291-297 (2001)

[文献書誌] 宮岡 礼子: "Lie sphere geometry and Lie contact structure"数理解析研究所講究録. 1150. 143-146 (2000)

[文献書誌] 宮岡 礼子: "Elie Cartanの業績-S. S. ChernとC. Chevaleyによる解説"数理解析研究所講究録. 1206. 1-31 (2001)

[文献書誌] 宮岡 礼子: "等径超曲面今昔-Elie Cartanと21世紀"数理解析研究所講究録. 1206. 32-44 (2001)

[文献書誌] 宮岡 礼子: "On special Lagragian submanifolds"数理解析研究所講究録. 1236. 1-8 (2001)

[文献書誌] 宮岡 礼子: "等径超曲面再訪"数学. 53. 18-33 (2001)

[文献書誌] 梅原 雅顕: "3次元双曲型空間における平坦な曲面"数理解析研究所講究録. 1236. 49-59 (2001)

[文献書誌] 金行壯二: "Recent Development in Geometry of Parahermitian Symmetric spaces"数理解析研究所講究録. 1150. 11-13 (2000)

[文献書誌] 相山玲子: "A construction of Lagrangian surfaces in the complex 2-space"数理解析研究所講究録. 1206. 121-133 (2001)

[文献書誌] 石川剛郎: "Recent Results on Developable Submanifolds : Examples and Classifications"数理解析研究所講究録. 1150. 134-141 (2000)

[文献書誌] J. Faraut: "Analysis And Geometry On Complex Homogeneous Domains Progress in Math vol.185"Birkhauser. (2000)

[文献書誌] 石川 剛郎: "代数曲線と特異点, 特異点の数理. 第4巻"共立出版. (2001)

2001 年度実績報告書

宮岡礼子上智大学, 理工学部, 教授 (70108182)

[文献書誌] 宮岡礼子: "Lie sphere geometry and Lie contact structure"数理解析研究所講究録. 1150. 143-146 (2000)

[文献書誌] 宮岡礼子: "Elie Cartanの業績-S. S. ChernとC. Chevaleyによる解説"数理解析研究所講究録. 1206. 1-31 (2001)

[文献書誌] 宮岡礼子: "等径超曲面今昔-Elie Cartanと21世紀"数理解析研究所講究録. 1206. 32-44 (2001)

[文献書誌] 宮岡礼子: "On special Lagragian submanifolds"数理解析研究所講究録. 1236. 1-8 (2001)

[文献書誌] 宮岡礼子: "等径超曲面再訪"数学. 53. 18-33 (2001)

[文献書誌] 梅原雅顕: "3次元双曲型空間における平坦な曲面"数理解析研究所講究録. 1236. 49-59 (2001)

[文献書誌] 石川剛郎: "代数曲線と特異点, 特異点の数理. 第4巻"共立出版. (2001)