1994 Fiscal Year Annual Research Report
| Project/Area Number |
06640160
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| Research Institution | Saga University |
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Principal Investigator |
石川 晋 佐賀大学, 理工学部, 助教授 (10039258)
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| Co-Investigator(Kenkyū-buntansha) |
神崎 正則 佐賀大学, 教養部, 教授 (70039262)
牧 春夫 佐賀大学, 教育学部, 教授 (60031788)
河合 茂生 佐賀大学, 教育学部, 助教授 (30186043)
亀谷 幸生 佐賀大学, 理工学部, 助手 (70253581)
町頭 義明 佐賀大学, 理工学部, 助手 (00253584)
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| Keywords | 有限型部分多様体 / 2重調和部分多様体 / アレクサンドロフ曲面 / モジュライ空間 / 共形計量 / チョウ形式 / ファジイ / 分枝過程 |
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| Research Abstract |
1.(1)n次元擬リーマン多様体Mからm次元擬ユークリッド空間E^m_‡への等長埋入写像xがΔ_2x=0の解であるとき,x(或いはM)を二重調和な擬リーマン部分多様体であるという.擬ユークリッド空間内の二重調和な擬リーマン部分多様体の分類問題について結果を得た.
(2)Mからm次元(擬)ユークリッド空間E^m_‡への等長埋入写像xがΔの固有ベクトルの有限和として表示できるとき,x(或いはM)を有限型部分多様体という.双曲型空間内の有限型曲線の分類問題について研究を進めた.
2.この研究課題による研究成果としては既に論文になったもの(裏面)以外に次の論文が準備中である.
(1)Y.Machigashira:The Gaussian curvature of Alexandrov surfaces
(2)Y.Machigashira:The total excess on length surfaces
(3)Y.Kametani:The simple invariant and differentiable structures on the Horikawa surface
(4)S.Hirose:Periodic automorphisms on surfaces and cobordism
(5)S.Hirose:A subgroup of mapping class group which leaves a standardly embedded surface invariant
(6)T.Tanaka:On explicit descriptions of Chow-forms
(7)H.Maki:Every topological space is pre-T_<1/2>
(8)M.Kosaki:On a certain harmonic property of generalised Fibonacci sequences
(9)M.Kosaki:On the asymptotic independence for diftusion processes on Riemannian manifolds
(10)Y.Ogura:Convergence of Riemannian metrirics and Diftusion processes
(11)Y.Ogura:A probabilistic scheme for collapse of metrics
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[Publications] B.Y.Chen and S.Ishikawa: "Biharmonic pseudo-Riemannian surfaces in pseudo-Euclidean spaces" Geometry,Number theory and Physics(Greece). To appear. (1995)
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[Publications] Y.Machigashira: "Complete open manifolds of non-negative radial curvature" Pacific Journal Mathematics. 165. 153-160 (1994)
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[Publications] Y.Kametani and Y.Sato: "O-dimensional Moduh Space of Stable Rank 2 Bundles and Differentiable Structures on Regular Elliptic Surfaces" Tokyo Journal of Mathematics. 17-1. 253-267 (1994)
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[Publications] Y.Kametani: "Simple Invariants of Homotopy Regular Elliptic Surfaces" Topology,geometry and field theory. 59-65 (1994)
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[Publications] Y.Kametani and Y.Nagatomo: "Classification of c_2-Self-Dual Bundles on a Quaternionic Projective Space" Osaka Journal of Mathematics. To appear. (1995)
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[Publications] S.Kawai: "Scalar curvature of conformal metrics on \S^n\" Nagoya Math.ematical Journal. 140. (1995)
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[Publications] H.Maki,R.Devi and K.Balachandran: "Associated topologies of Generalized ＼alpha-closed and ＼alpha-generalized closed sets" Memoirs of the Faculty of Science,Kochi University,Ser.A,Mathematics. 15. 51-63 (1994)
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[Publications] R.Devi,K.Balachandran and H.Maki: "Semi-Generalized homeomorphisms and generalized semi-homeomorphisms in topological spaces" Indian Journal of Pure and Applied Mathematics. (To appear). (1995)
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[Publications] Y.Ogura,H.M.Ito and M.Tomisaki: "Some asymptotic theorems of one-dimensional generalized diffusion processes and their applications to statistical physics" Trends in Statistical Physics. (To appear). (1995)
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[Publications] Y.Ogura,K.Handa and P.Kalukottege: "A probabilistic interpretation of the degree of fuzziness" Journal of Appl.Probability. 31. 1034-1148 (1994)
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[Publications] 今村 雅,神崎正則 中原 徹: "円形パズルと法mに関するフィボナッチ数列の周期現象" 佐賀大学理工学部集報. 22. 169-185 (1994)
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[Publications] 神崎正則,中原 徹: "フィボナッチ数列の周期" 数理科学. 376. 86-91 (1994)
