2000 Fiscal Year Annual Research Report

微分式系と部分多様体論

Research Project

Project/Area Number	12640087
Research Institution	Sophia University
Principal Investigator	宮岡礼子上智大学, 理工学部, 教授 (70108182)
Co-Investigator(Kenkyū-buntansha)	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) 金行壮二上智大学, 理工学部, 教授 (40022553) 梅原雅顕広島大学, 理学部, 教授 (90193945) 横山和夫上智大学, 理工学部, 助教授 (10053711)
Keywords	等径超曲面 / 主曲率 / 重複度 / ガウス写像 / 退化 / スペシャルラグランジアン部分多様体 / 平均曲率一定曲面 / 調和写像
Research Abstract	等径超曲面の主曲率が6個の分類にとりくみ,重複度1の時の等質性の新しい幾何学的証明を与えた.重複度2は進行中である.また,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まとめた.ここでは,スペシヤルラグランジアン部分多様体との関係があらわれ興味深いので,引き続き研究する.また,リーの球幾何学と,リー接触構造の研究を続ける上で,今までの結果をまとめた.さらに分担者,芥川(相山)玲子,梅原雅章らとは,3次元球面の平均曲率一定曲面のガウス写像の2つの調和写像への分解の逆問題として,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た. 石川剛郎は,空間曲線の可展面の位相的分類を与えた.芥川(相山)はKenmotsu type,Bryant typeの曲面の表現公式を任意の空間型の中で構成した.梅原は,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,曲面上の円周束のよい埋め込みを考えた.宇田川はエルミート対称空間内の円の研究をした.金行はパラエルミート対称空間の基礎およびその応用の研究を続行中である.内山康一はp楕円型方程式の1次元モデルである非線形常微分方程式の固有関数の特異性の局所表示を確定特異点をもつ非線形常微分方程式の正則解に帰着して考察した。横山和夫はDSダイアグラムをもちいる3次元位相多様体の研究において,どんなDSダイアグラムもE-cycleをもつものとDS同型であることを示した.

Research Products
(20 results)

All Other

All Publications (20 results)

[Publications] R.Aiyama: "Aglohal crrespondence between CMC-surfaces in S^3 and pain of non-conformal harmonic mops in liS^2"Proc.Amer.Math.Soc.. 128. 939-941 (2000)
[Publications] R.Miyaoka: "A simple proct of the homogeneity of isoparametric hyper surfaces with (g.m)=(6.1)"Geometry and Topology of Submamifolds. X. 178-199 (2000)
[Publications] R.Miyaoka: "Lie spheare geometry and Lie contact structures"数理解析研究所講究録. 1150. 143-146 (2000)
[Publications] 宮岡礼子: "等径超曲面再訪"数学. 53. 18-33 (2001)
[Publications] Goo Ishikawa: "Topological classification of the tangent developables of a nace curres"Jour.of London Math.Soc.. 62. 583-598 (2000)
[Publications] H.Ikeda: "Remodelings DS-diagram into one with E-cycle Tokyo Jour.Hath."
[Publications] Goo Ishikawa : "Solution surfaces of monge-Ampire equation"Diff.Geom.and Appl.. (to appear). (2001)
[Publications] R.Aiyama: "Kenmoteu tyre represeritations for mula for surfaces with prescribed mean curvature in the 3-sphere"Tohokci Math.J.. 52. 95-105 (2000)
[Publications] R.Aiyama: "Kenmoten tyre represeritation for mula for space like surfaces with prescribed mean curvature in the de Sittu 3-space"Tsukuha J.Math. 24. 189-196 (2000)
[Publications] R.Aiyama: "Minimal mops Between hyperbolic dish and generalized Gaussmans of maximal surfaces in the anti de sitter 3-spaces"Tohoka J,Math. 52. 415-429 (2000)
[Publications] R.Aiyama: "Kenmotsu tyre represeritation for mula for surfaces with prescribed mean curvature -in the hyperbolic 3-space"J.Math.Soc.Japan. 52. 877-898 (2000)
[Publications] S.Kaneyuki: "Comfactification of parahermitian symmetri spaces and its application"Lie Theory and its Application in Physics. 63-74 (2000)
[Publications] S.Kato: "General existence of minimal surfaces of genus zero with catenoidal ends and prescribed flux"Comm.Analy and Geom.. 8. 83-114 (2000)
[Publications] M.Umehare: "Metrics of constand curvature 1 with three conical singularities on the 2-sphere"Fllinois J.of Math.. 44. 72-94 (2000)
[Publications] M.Kumura: "Minimal immesscions of some cricle bandle over holomorphic curves in complex quadric to sphere"Osaha.Math.J.. 37. 883-903 (2000)
[Publications] T.Adachi: "Simpleness and closedness of circles in compact Hermitian symmetric spaces"Tsukuha J.Math.. 24. 1-13 (2000)
[Publications] K.Balachandran: "Existence of solutions of nonlinear integro differential equations of Sobolev type with nonlocal condition in Banach spaces "Proc.Indian Acad.Sci.. 110. 225-232 (2000)
[Publications] K.Balanchamdran : "Existence of solutions of quanilinear integrodifferential equations with nonlocal condition"Tokyo J.Math. 23. 203-210 (2000)
[Publications] G.Ishikura: "Submanifolds with degenerate Gauss mapping"Josai Mathematical monograph 3,Differential Geometry. 3. 125-138 (2001)
[Publications] I.Faraut: "Analysis and Geometry on Complex Homogeneous Domains."Progress in Math.,Birkhanser.. 540 (2000)

2000 Fiscal Year Annual Research Report

微分式系と部分多様体論

Principal Investigator

宮岡 礼子 上智大学, 理工学部, 教授 (70108182)

Research Products

[Publications] R.Aiyama: "Aglohal crrespondence between CMC-surfaces in S^3 and pain of non-conformal harmonic mops in liS^2"Proc.Amer.Math.Soc.. 128. 939-941 (2000)

[Publications] R.Miyaoka: "A simple proct of the homogeneity of isoparametric hyper surfaces with (g.m)=(6.1)"Geometry and Topology of Submamifolds. X. 178-199 (2000)

[Publications] R.Miyaoka: "Lie spheare geometry and Lie contact structures"数理解析研究所講究録. 1150. 143-146 (2000)

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

[Publications] Goo Ishikawa: "Topological classification of the tangent developables of a nace curres"Jour.of London Math.Soc.. 62. 583-598 (2000)

[Publications] H.Ikeda: "Remodelings DS-diagram into one with E-cycle Tokyo Jour.Hath."

[Publications] Goo Ishikawa : "Solution surfaces of monge-Ampire equation"Diff.Geom.and Appl.. (to appear). (2001)

[Publications] R.Aiyama: "Kenmoteu tyre represeritations for mula for surfaces with prescribed mean curvature in the 3-sphere"Tohokci Math.J.. 52. 95-105 (2000)

[Publications] R.Aiyama: "Kenmoten tyre represeritation for mula for space like surfaces with prescribed mean curvature in the de Sittu 3-space"Tsukuha J.Math. 24. 189-196 (2000)

[Publications] R.Aiyama: "Minimal mops Between hyperbolic dish and generalized Gaussmans of maximal surfaces in the anti de sitter 3-spaces"Tohoka J,Math. 52. 415-429 (2000)

[Publications] R.Aiyama: "Kenmotsu tyre represeritation for mula for surfaces with prescribed mean curvature -in the hyperbolic 3-space"J.Math.Soc.Japan. 52. 877-898 (2000)

[Publications] S.Kaneyuki: "Comfactification of parahermitian symmetri spaces and its application"Lie Theory and its Application in Physics. 63-74 (2000)

[Publications] S.Kato: "General existence of minimal surfaces of genus zero with catenoidal ends and prescribed flux"Comm.Analy and Geom.. 8. 83-114 (2000)

[Publications] M.Umehare: "Metrics of constand curvature 1 with three conical singularities on the 2-sphere"Fllinois J.of Math.. 44. 72-94 (2000)

[Publications] M.Kumura: "Minimal immesscions of some cricle bandle over holomorphic curves in complex quadric to sphere"Osaha.Math.J.. 37. 883-903 (2000)

[Publications] T.Adachi: "Simpleness and closedness of circles in compact Hermitian symmetric spaces"Tsukuha J.Math.. 24. 1-13 (2000)

[Publications] K.Balachandran: "Existence of solutions of nonlinear integro differential equations of Sobolev type with nonlocal condition in Banach spaces "Proc.Indian Acad.Sci.. 110. 225-232 (2000)

[Publications] K.Balanchamdran : "Existence of solutions of quanilinear integrodifferential equations with nonlocal condition"Tokyo J.Math. 23. 203-210 (2000)

[Publications] G.Ishikura: "Submanifolds with degenerate Gauss mapping"Josai Mathematical monograph 3,Differential Geometry. 3. 125-138 (2001)

[Publications] I.Faraut: "Analysis and Geometry on Complex Homogeneous Domains."Progress in Math.,Birkhanser.. 540 (2000)

宮岡礼子上智大学, 理工学部, 教授 (70108182)