Research on classical differential geometry from modern view points and its applications

2014 Fiscal Year Final Research Report

• Project/Area Number: 22540107
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Geometry
• Research Institution: Kwansei Gakuin University (2011-2014); Fukuoka University (2010)
• Principal Investigator: KUROSE Takashi 関西学院大学, 理工学部, 教授 (30215107)
• Co-Investigator(Renkei-kenkyūsha): SUYAMA Yoshihiko 福岡大学, 理学部, 教授 (70028223) ; HAMADA Tatsuyoshi 福岡大学, 理学部, 助教 (90299537) ; KAWAKUBO Satoshi 福岡大学, 理学部, 助教 (80360303) ; MATSUURA Nozomu 福岡大学, 理学部, 助教 (00389339) ; INOGUCHI Junichi 山形大学, 理学部, 教授 (40309886) ; FURUHATA Hitoshi 北海道大学, 大学院理学研究院, 准教授 (80282036) ; FUJIOKA Atsushi 関西大学, システム理工学部, 教授 (30293335)
• Project Period (FY): 2010-04-01 – 2015-03-31
• Keywords: 古典的微分幾何 / 曲線の運動 / 可積分系方程式 / 多重ハミルトン系 / 統計多様体 / ヘッセ多様体 / ヘッセ断面曲率

Outline of Final Research Achievements

In this research program, classical differential geometry, geometry of curves, surfaces and hypersurfaces in various spaces, have been studied, mainly with the method of the theory of integrable systems. Many results on classical differential geoemtry and its application have been achieved; for instance, through the observation that certain sorts of changes with time of curves yield equations dealt with in the theory of integrable systems, geometric descriptions and/or interpretations of several accomplishments of the theory have been given. Moreover, by applying geometry of hypersurfraces in affine spaces, new properties of statistical manifolds, which appear in informtion geometry, the study of mathematical statistics and information theory with differential geometric tools and methods, have been obtained and the statistical manifolds satisfying some curvature condition have been explicitely constructed and classified.

Free Research Field

微分幾何