2012 Fiscal Year Final Research Report
Research of submanifolds in symmetric spaces by usingthe infinite dimensional geometry and the complexification
| Project/Area Number |
21540095
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
Geometry
|
|---|
| Research Institution | Tokyo University of Science |
|---|
Principal Investigator |
KOIKE Naoyuki 東京理科大学, 理学部第一部数学科, 准教授 (00281410)
|
|---|
| Project Period (FY) |
2009 – 2012
|
| Keywords | 部分多様体幾何 / リ-群作用 / 平均曲率流 / 対称空間 / 無限次元幾何 / 複素化 |
|---|
| Research Abstract |
Main results of this research are as follows.
(1) We showed that complex equifocal submanifolds in a symmetric space of non-compact type are congruent to principal orbits of Lie group actions called “Hermann action” under certain conditions.
(2) We showed that non-minimal equifocal submanifolds in a symmetric space of compact type collapse to their focal submanifolds along the mean curvature flow.
(3) We investigated the regularized mean curvature flow for invariant hypersurfaces in a Hilbert space equipped with a Hilbert Lie group free action and proved a certain kind of strongly convex preservability theorem for the flow.
(4) We classified hyperpolar actions on symmetric spaces of non-compact type under some conditions.
|
