2010 Fiscal Year Final Research Report
Riemannian homogeneous spaces and their Grassmann geometry
| Project/Area Number |
20540078
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
Geometry
|
|---|
| Research Institution | Yamaguchi University |
|---|
Principal Investigator |
NAITO Hiroo Yamaguchi University, 大学院・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, 准教授 (50180237)
ANDO Yoshifumi 山口大学, 名誉教授 (80001840)
WATANABE Tadashi 山口大学, 教育学部, 教授 (10107724)
|
|---|
| Co-Investigator(Renkei-kenkyūsha) |
KOMIYA Katsuhiro 山口大学, 名誉教授 (00034744)
|
|---|
| Project Period (FY) |
2008 – 2010
|
| Keywords | 対称空間 / 等質空間 / 部分多様体 / グラスマン幾何 / リー理論 |
|---|
| Research Abstract |
In the study of Riemannian geometry, a Riemannian symmetric space is one of the most important spaces and homogeneous submanifolds of Riemannian symmetric spaces often appear in the study of its submanifold theory as typical examples of subspaces. Therefore, the classification of homogeneous submanifolds is one of important problems to solve. In order to approach the classification problem, in this research we introduce an analytic method called Grassmann geometry, which is based on the theory of partial differential equations, and by applying it to surfaces of the 3-dimensional unimodular Lie groups with left invariant metric, which are in general not Riemannian symmetric spaces but homogeneous Riemannian manifolds, we investigate the effort of Grassmann geometry for the submanifold theory of Riemannian symmetric spaces.
|
