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首页> 外文期刊>The Asian journal of mathematics >COLLAPSE OF THE MEAN CURVATURE FLOW FOR EQUIFOCAL SUBMANIFOLDS
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COLLAPSE OF THE MEAN CURVATURE FLOW FOR EQUIFOCAL SUBMANIFOLDS

机译:等曲子流形的平均曲率流崩溃

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In this paper, we investigate the mean curvature flows having an equifocal submanifold in a symmetric space of compact type and its focal submanifolds as initial data. It is known that an equifocal submanifold of codimension greater than one in an irreducible symmetric space of compact type occurs as a principal orbit of a Hermann action. However, we investigate the flows conceptionally without use of this fact. The investigation is performed by investigating the mean curvature flows having the lifts of the submanifolds to an (infinite dimensional separable) Hilbert space through a Riemannian submersion as initial data.
机译:在本文中,我们研究了在紧凑型对称空间中具有等焦点子流形的平均曲率流及其焦点子流形作为初始数据。众所周知,在紧型的不可约对称空间中,余维的等焦点子流形大于一,这是赫曼作用的主轨道。但是,我们从概念上研究了流量,而没有利用这一事实。通过研究具有子流形升程到(无限维可分离)希尔伯特空间的平均曲率流,通过黎曼浸入作为初始数据进行研究。

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