Grassmann geomety of surfaces in a Riemannian symmetric space

2014 Fiscal Year Final Research Report

• Project/Area Number: 23540091
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Geometry
• Research Institution: Yamaguchi University
• Principal Investigator: NAITOH Hiroo 山口大学, 理工学研究科, 教授 (10127772)
• Co-Investigator(Kenkyū-buntansha): NAKAUCHI Nobumitsu 山口大学, 大学院理工学研究科, 教授 (50180237) ; KAJI Shizuo 山口大学, 大学院理工学研究科, 講師 (00509656) ; KAWAKAMI Yu 金沢大学, 数物科学系, 准教授 (60532356) ; KONDO Kei 山口大学, 大学院理工学研究科, 准教授 (70736123)
• Project Period (FY): 2011-04-28 – 2015-03-31
• Keywords: 対称空間 / 曲面論 / グラスマン幾何 / リー理論

Outline of Final Research Achievements

In Riemannian geometry, a Riemannian symmetric space is one of the most important spaces and in the study of submanifolds in it, the classification problem of homogeneous submanifolds is also one of important open problems to solve. As an approach to this problem, the aim of this study is to consider many kinds of surfaces in a Riemannian symmetric space from the standpoint of Grassmann geometry, which may be described in terms of the system of 1st order partial differential equations, and to find out all the sustantial theories of Grassmann-geometric surfaces in a Riemannian symmetric space. As a research result, we have obtained the classification of all formal theories of Grassmann-
geometric surfaces and an expectation that the substantial theories may be found out in terms of a certain kind of cohomology theory among the formal theories of Grassmann-geometric surfaces. But we can not establish a theory yet.

Free Research Field

微分幾何