多様体の幾何学に関する総合的研究

1992 Fiscal Year Annual Research Report

• Project/Area Number: 03302002
• Research Institution: NIIGATA UNIVERSITY
• Principal Investigator: 関川 浩永 新潟大学, 理学部, 教授 (60018661)
• Co-Investigator(Kenkyū-buntansha): 大森 英樹 東京理科大学, 理工学部, 教授 (20087018) ; 坂根 由昌 大阪大学, 理学部, 助教授 (00089872) ; 塩浜 勝博 九州大学, 理学部, 教授 (20016059) ; 西川 青季 東北大学, 理学部, 教授 (60004488) ; 砂田 利一 東京大学大学院, 数理科学研究科, 教授 (20022741)
• Keywords: リーマン多様体 / 調和写像 / スペクトラム / 平均曲率 / アインシュタイン計量 / ゲージ理論 / ケーラー多様体 / ハミルトニアン

Research Abstract

多様体の幾何学は微分幾何学のみならず、数学の各分野及び数理物理学、工学、情報科学における研究とも不深く関わりを持っており、現在活発に研究されている。このため、多様体の幾何学について様々な角度から総合的に研究することをその目的とした。この研究目的を達成するため、(1)大域解析学、(2)リーマン幾何学、(3)部分多様体論及びテンソル幾何学、(4)多様体上の幾何学的構造、(5)複素幾何学、及び(6)多様体上の力学及び力学系の側面からの研究の6つの研究プロジェクトを設け、各研究プロジェクト間の研究連絡及び情報交換を通して研究を遂行した。(1)においては、調和写像についてその存在及び安定性、また、ツイスター対応を用いた調和写像の具体的構成やゲージ理論の低次元トポロジーへの応用等に関して、(2)においては非正リーマン多様体及びひコンパクト・リーマン多様体の構造についての無限遠点の幾何の立場からの研究において、またGromovの収束定理に係わる諸問題について、さらに山辺不変量と関連した不変量に関する研究及び共形平担リーマン多様体の構造について、(3)においては、平均曲率一定の曲面(極小曲面を含む)について、(4)においては、多様体上の微分方程式の幾何学的取扱いに関する研究について、(5)においては、二本不変量とその周辺に関する話題について、またケーラー・アインシュタイン構造の存在(その構成も含む)、及びモジュライ空間の位相等について、(6)においては、ハミルトン力学系及びその量子化に関連した話題について、例えば、Liouville-Arnoldの定理の一般化や、統計学における力学的側面からの研究及び複数の研究プロジェクトに渡る研究に関して各々、多くの重要な研究成果を得ている。

Research Products

• [Publications] 文部 孝順: "On closed regular curves in Riemannian manifolds" Nihonkai Math.J.2. 47-61 (1991)
• [Publications] 阿部 孝順: "On closed regular curves and fundamental from on the projective spaces" Proc.Japan Acad.68. 123-125 (1992)
• [Publications] 阿部 直人: "Multi-curvature forms and their apolications to dual connections" SUT Journal of Math. 27. 229-235 (1991)
• [Publications] 足立 俊明: "Spherical mean and the fundamental group" Canad.Math.Bull.34. 3-11 (1991)
• [Publications] 足立 俊明: "The Euclidean factor a Hadamard manifold" Proc.AMS. 113. 209-213 (1991)
• [Publications] 阿賀岡 芳夫: "Generalized Gauss equations" Hokkaido Math.J.20. 1-44 (1991)
• [Publications] 愛甲 正: "On complex Finsler manifolds" Rep.Fac.Sci.Kagoshoma Univ.24. 9-25 (1991)
• [Publications] 相山 玲子: "On complete speace-like surfaces with constant mean curvature in a Lorentzian 3-space Form" Tsukuba J.Math.15. 235-247 (1991)
• [Publications] 赤堀 隆夫: "On the Romanov kernel and Kuranishi's L_2 estimate For ∂_b over a ball in the strongly pseudo convex boundary" Pacific J.Math.149. 1-12 (1991)
• [Publications] 赤堀 隆夫: "On the construction of the moduli space for strongly pseudoconvex domains" Proc.Symposia in Pure Math.52. 53-58 (1991)
• [Publications] 赤堀 隆夫: "A criterion for versality of deformations of tubular neighborhborhoods of strongly pseudo convex boundaries" Can.J.Math.44. 1-9 (1992)
• [Publications] 明山 浩: "Stochastic flows of automorphisms of G-structures of degree r" Proc.Japan Acad.67. 45-48 (1991)
• [Publications] 厚山 健次: "Projective spaces in a wider sense,I" Kodai Math.J.15. 324-340 (1992)
• [Publications] 厚山 健次: "Simple Lie algebras and projective planes in a wider sense" “Non associative algevras and related topics". 9-18 (1991)
• [Publications] 坂東 重稔: "Removable singularities for holomorphic vector bundles" Tohoku Math.J.43. 61-67 (1991)
• [Publications] 江口 正晃: "The explicit representation of the determinant of Harish-Chandra's C function in SL(3,R)and SL(4,R) cases" Hiroshima Math.J.22. 57-93 (1992)
• [Publications] 江口 正晃: "An explicit expression of the HarisH-Chandra C-fandre C-function of SU(n,1) associated to the Ad(K) representation" Proc.Japan Acad.68. 232-236 (1992)
• [Publications] 江口 真透: "A geometric look at nuisance parameter effect of local powers in testing hypothesis" Ann.Inst.Statist.Math.43. 245-260 (1991)
• [Publications] 江口 真透: "The Projection method for accelerated life test model in bivariate exponential distributions" Mem.Fac.Sci.Shimane Univ.25. 15-19 (1992)
• [Publications] 江口 真澄: "Geomety of minimum contrast" In press in Hiroshima Math.J.22. 631-647 (1992)
• [Publications] 江尻 典雄: "Two applications of the unit normal bundle of a minimal surface in R^N" Pacific J.Math.147. 291-300 (1991)
• [Publications] 江尻 典雄: "Minimal surfaces in S^<2m>(1) with extra eigenfunctions" Quart.J.Math.Oxford. 43. 421-440 (1992)
• [Publications] 榎本 一之: "Compactification of asymptitically umbilical hypersurfaces in hyperbolic space" Mem.Fac.Sci,Kyushu Univ.,Ser.A. 46. 57-68 (1992)
• [Publications] 藤本 坦孝: "Modified defect relations for the Gauss map of minimal surfaces,III" Nagoya Math.Journal. 124. 13-40 (1991)
• [Publications] 藤本 坦孝: "On the Gauss curvature of minimal surfaces" J.Math.Soc.Japan. 44. 427-439 (1992)
• [Publications] 深谷 賢治: "Nilpotent structure and invariant metrics on Collapsed manifolds" Journal of AMS.5. 327-372 (1992)
• [Publications] 深谷 賢治: "Almost nonpositively curved manifolds" J.Differential Geometry. 33. 69-90 (1991)
• [Publications] 二木 昭人: "A Lie algebra character and Kahler-Einstein metrics of positive scalar curvature" Proc.Symp.Pure Math.52. 209-215 (1991)
• [Publications] 二木 昭人: "ケーラー多様体と積分不変量" 数学. 44. 44-56 (1992)
• [Publications] 木村 真琴: "On real hypersurfaces of a complex projective space II" Tsukuba.Math.15. 547-561 (1991)
• [Publications] 清原 一吉: "Compact Liouville surfaces" J.Math.Soc.Japan. 43. 555-591 (1991)
• [Publications] 小林 亮一: "Holomorphic curves into algebraic subvarieties in an Abelian variety" International Journal of Math.2. 711-724 (1991)
• [Publications] 古田 高士: "Geometry of SU(2)×SU(2)×U(1)/U(1)×U(1)" Math.J.Toyama University. 14. 193-207 (1991)
• [Publications] 小池 直之: "Foliations on a Riemannian manifold and Ehresmann connections" Indiana Univ.Math.J.40. 277-292 (1991)
• [Publications] 小磯 憲史: "Motion of a springy circle wire" Sci.Rep.Col.Gen.Educ.Osaka Univ.40. 15-19 (1991)
• [Publications] 小磯 憲史: "Elasticae in Riemannian submanifold" Osaka J.Math.20. 643-649 (1991)
• [Publications] 桑原 類史: "A note on the deformations of Hamiltonian systems on nilmanifolds" J.Math.Tokushima Univ.26. 19-29 (1992)
• [Publications] 満渕 俊樹: "Stabiluty and Einstein-Kahler metric of a quartic del Pezzo surface" “Einstein metrics and Yang-Mills connections"Lecture notes in Pure and Appl.Math.133-160 (1993)
• [Publications] 前田 正男: "The classification of compact surfaces by using Berger's lemma" Mem.Fac.Sei.Kyushu Univ.,Ser.A. 46. 201-215 (1992)
• [Publications] 前田 正男: "Compact surfaces of type 2" Sei.Rep.Yokohama Nat.Univ.Sec.I. 39. 13-16 (1992)
• [Publications] 前田 定広: "On real of a complex projective space II" Tsukiba J.Math. 15. 547-561 (1991)
• [Publications] 前田 吉郎: "Weyl manifold and deformation quantization" Advance in Mathematics. 85. 224-255 (1991)
• [Publications] 前田 吉昭: "Global calculus on Weyl manifolds" Japan Journal of Math.17. 57-82 (1991)
• [Publications] 前田 吉昭: "Deformation quantization of Posson algebras" Proceedings of Japan Academy. 68. 97-100 (1992)
• [Publications] 間下 克哉: "On the stability of Cartan embedings of compact symmetric spaces" Arch.Math.58. 500-508 (1992)
• [Publications] 松田 博男: "Homogeneous Lorentz manifolds with isotropy subgroup U(2) or SO(2)" Tsukuba J.Math.16. 257-267 (1992)
• [Publications] 松本 紘司: "A certain symmetric F-connection in locally conformal Kahler space form" Bull.of Yamagata Univ.(Nat.Sci). 13. 1-11 (1992)
• [Publications] 松本 誠: "A left transformation preserving a Finsler connection invariant" Publ.Math.,Debrecen. 38. 77-82 (1991)
• [Publications] 松本 誠: "On integral manifolds of an integrable nonliner connection form the stand-point of the theory of Finsler connections" J.Math.Kyoto Univ.31. 835-843 (1991)
• [Publications] 松本 誠: "Projectively flat Finslr spaces with (α,β)-metric" Reports on Math.Phys.30. 15-20 (1991)
• [Publications] 松本 誠: "Finsler space of constant curvature with Kropina metric" Tensor,N.S.50. 194-201 (1991)
• [Publications] 後藤 亨: "On some differential geometric geometric characterizations of the center of a Lie group" Tokyo Journal of Math.14. 305-308 (1991)
• [Publications] 後藤 亨: "A remark on foliations on a complex projective space with complex leaves" Tsukuba Journal of Math.16. 169-172 (1992)
• [Publications] 長谷川 和泉: "Cyclic parallel hypersurfaces in a Sasakian space form" J.Hokkaido Univ.Ed.(Sect.IIA). 41. 1-15 (1991)
• [Publications] 橋口 正夫: "On the Gaussian curvature of the indicatrix of a Lagrangian" Rep.Fac.Sci.Kagoshima Univ.24. 33-41 (1991)
• [Publications] 橋本 英哉: "Oriented 5-dimensional submanifolds in the purely imaginary octonians" J.Korean Math.Soc.128. 167-182 (1991)
• [Publications] 市田 良輔: "A certain inequality on Riemannian manifolds of projective curvature" Memoirs of the Faculty of Science,Kyushu Univ.46. 105-114 (1992)
• [Publications] 一條 義博: "Conformally flat Finsler structures" J.Math.Tokushima Univ.25. 13-26 (1991)
• [Publications] 池田 章: "Zeta functions for differential forms on complex projective spaces and their asymptotic expansions" Bull.Fac.Sch.Educ.Hiroshima Univ.13. 1-10 (1991)
• [Publications] 印南 信宏: "Riemannian metric having poles and nonpoles on surfaces" Mem.Fac.Sci.Kyushu Univ.Ser.A. 46. 79-84 (1992)
• [Publications] 印南 信宏: "Jacobi vector Fields along geodesic flows" Dynamical System and Related Topics,World Scientific Adv.,Ser.in Dynam.Sys.9. 166-174 (1991)
• [Publications] 石原 徹: "Harmonic maps of nonorientable surfaces to four dimensional manifold" Tohoku Math.J.45. 543-559 (1993)
• [Publications] 石川 晋: "Biharmonic surfaces in pseudo-Euclidean spaces" Memoirs of Fac.Sci.,Kyushu Univ.,Ser.A. 45. 325-349 (1991)
• [Publications] 石川 晋: "Biharmonie W-Surfaces in 4-dimensional pseudo-Euclidean space" Memoris of Fac.Sci.,Kyushy Univ.,Ser.A. 46. 266-286 (1992)
• [Publications] 伊藤 良彦: "日本における微分積分に関するカリキュラムの変遷" 早稲田大学数学教育学会誌. 9. 27-30 (1991)
• [Publications] 伊藤 光弘: "Yanabe metrics and the space of conformal structures" International Jour.Math.2. 659-671 (1991)
• [Publications] 伊藤 武広: "Complete surfaces in E^3 with constant mean curvature" Tamkang J.22. 79-82 (1991)
• [Publications] 岩井 敏洋: "The MIC-Kepler problem and its symmetry group for positive energies both in classical and quantum mechanics" Nuovo Cimento. 106B. 849-871 (1991)
• [Publications] 岩井 敏洋: "The MIC-Kepler problem and its symmetry group for zero energy both in classical and quantum mechanics" Nuovo Gimento. 106B. 1195-1219 (1991)
• [Publications] 岩井 敏洋: "A representation of the Guichardet connections in the Aharoniv-Anandan connection" Physics Letters A. 162. 289-293 (1992)
• [Publications] 岩井 井洋: "Berry connections as Yang-Mills Connections on CP^2" Physics Letters A. 166. 89-93 (1992)
• [Publications] 井関 裕靖: "On the conformal transformation grop of a compact Riemannian manifold with constant scalar curvature" Tokyo Journal of Math.15. 123-127 (1992)
• [Publications] 井関 裕靖: "On compact conformally flat 4-manifolds" Tohoku Math.Journal. 44. 299-304 (1992)
• [Publications] 金行 壯二: "Homogeneous symplectic manifolds and dipolarizations in Lie algebras" Tokyo J.Math.15. 279-291 (1992)
• [Publications] 金行 壯二: "On the subalgebras go and gev of semisimple graded Lie algebras" J.Math.Soc.Japan. 45. 1-19 (1993)
• [Publications] 河口 知商: "Sur la theorie geometrique de la optique relativiste" Comptes Rendus Hebdomadaires des Seances de I'Academie des Sciences. 312. 593-598 (1991)
• [Publications] 河口 知商: "On the relativistic geometrical optics" International Journal of Theoretical Physics. 30. 1521-1543 (1991)
• [Publications] 河知 知商: "Generalized Lagrange metric derived from a Finsler function" Reports on Math.Physics. 30. 41-52 (1991)
• [Publications] 河口 知商: "Finslerian approach to lagrange mechanics" Colloquia Math.Soc.Janos Bolyai. 56. 1-5 (1991)
• [Publications] 河口 知商: "Anomalously-Finslerian corrections to speed-of-light given by metric tensor g_<ij>(x,x)=r_<ij>+i_ii_i" Tensor,N.S.51. 170-176 (1991)
• [Publications] 河合 茂生: "On the Dirichlet problem of the equation-Δu=Ku^5 on the ball in R^3" Funkcialaj Ekvacioj. 35. 321-331 (1992)
• [Publications] 河合 茂生: "Concerning a type of Sobolev inequality on the sphere" Math.Ann.293. 7-16 (1992)
• [Publications] 剱持 勝衛: "Foliations by hypersurfaces with constant mean curvature" Math.Zeit.207. 97-108 (1991)
• [Publications] 吉川 通彦: "Projectivity of homogeneous left loop" Proc.Intetnational Symposium on Nonassociative Algebras and Related Topics,Hiroshima,1990. 77-99 (1991)
• [Publications] 吉川 通彦: "A class of double Lie algebras on simple Lie algebras and projectivity of simple Lie groups" Mem.Fac.Sci.Shimane Univ.25. 39-44 (1991)
• [Publications] 吉川 通彦: "Symmetrizability of geodesic homogeneous left Lie loops" Proc.3rd Geometry Conference Thessaloniki 1991. 230-238 (1992)
• [Publications] 菊地 重隆: "Legendre transformations of the generalized Lagrange space" Tensor. 50. 177-182 (1991)
• [Publications] 松本 誠: "A special class of locally Minkowski spaces with(α,β)-metric and conformally flat Kropina spaces" Tensor,N.S.50. 202-207 (1991)
• [Publications] 松本 正恒: "New equations on n-dimensional almost Tachibana spaces" Bull.st.Marianna Univ.20. 5-12 (1991)
• [Publications] 岩本 正恒: "On linked vector patterns and constellation graph" Bull.st.Marianna Univ.20. 13-18 (1991)
• [Publications] 松本 正恒: "On linked vector Patterns for rank data" Bull.st.Marianna Univ.21. 7-12 (1992)
• [Publications] 松永 弘道: "Note on periodic instanton" Mem.Fac.Sci.Shimane Univ.25. 1-5 (1991)
• [Publications] 松下 泰雄: "Fields of 2-planes and two kinds of almost complex structures on compact 4-dimensional manifolds" Math.Z.207. 281-291 (1991)
• [Publications] 松山 善男: "On symmetric spaces admitting a conformally flat hypersurfaces" Bull.Facul.Sci.and Eng.Chuo Univ.34. 1-23 (1991)
• [Publications] 三上 健太郎: "Symplectic double groupoids over Posson (ax+b)-groups" Trans.Amer.Math.Soc.324. 447-463 (1991)
• [Publications] 三村 文武: "Alternative approach to the inverse problem of Lagrangian dynamics in the multiple variational principle" Bull.Kyushu Inst.Tech.Math.Natur.Sci.38. 1-12 (1991)
• [Publications] 三村 文武: "Conservation laws of one-dimensional nonconservative motions" Bull.Kyusyu Inst.Tech.Math.Natur.Sci.39. 9-27 (1992)
• [Publications] 三村 文武: "Conditions for deriving conservation law in nonconservative Lagrangian dynamics" Tensor,N.S.51. 165-169 (1992)
• [Publications] 三村 文武: "Extended derivations associated with vector-valued differential forms" Tensor,N.S.51. 169-207 (1992)
• [Publications] 河口 知商: "数理情報辞典,フィッシャーの情報量について" 朝倉書店, (1993)
• [Publications] 大森 英樹: "一般力学系と場の幾何学" 裳華房, 317 (1991)
• [Publications] 酒井 隆: "リーマン幾何学(数学選書11)" 裳華房, 421 (1992)
• [Publications] 早根 由昌: "Complex Geometry" Proceedings of the Osaka International conference,Marcel Dekker, 240 (1992)
• [Publications] 竹内 勝: "Lie Groups I" Amer.Math.Soc, 112 (1991)
• [Publications] 竹内 勝: "Lie Groups II" Amer.Math.Soc., 147 (1991)