报告题目: |
Weakly reflective submanifolds and austere submanifolds |
报告人: |
Takashi SAKAI |
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Prof. Osaka City University Advanced Mathematical Institute, Japan
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报告时间: |
2008-12-29 09:40 |
报告地点: |
理科楼1304报告厅 |
主办单位: |
数学科学系 |
简介: |
Harvey-Lawson introduced the notion of an austere submanifold, which is a minimal submanifold whose second fundamental form has a certain symmetry.In this talk, we give a classification of all austere orbits of $s$-representations,that are linear isotropy representations of Riemannian symmetric pairs. Since the definition is focused on a symmetry of its second fundamental form,the notion of an austere submanifold is an infinitesimal property of a submanifold. However, we observe that some of austere orbits which we classified have a certain global symmetry.This symmetry is a globalization of the notion of an austere submanifold and a weakened condition of a reflective submanifold.Therefore we shall call them weakly reflective submanifolds, and study some fundamental properties of them. Finally we determine all weakly reflective orbits
of $s$-representations.
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