Collapse of the mean curvature flow for equifocal submanifolds

Details Collapse of the mean curvature flow for equifocal submanifolds Collapse of the mean curvature flow for equifocal submanifolds

2009-08-21

arxiv.org/abs/0908.3086v5

Asian Journal of Mathematics vol. 15 (2011) 101-128

Mathematics

Differential Geometry

31pages

Scientific paper

In this paper, we investigate the mean curvature flows for an equifocal submanifold in a symmetric space of compact type and its focal submanifolds as initial data. It is known that equifocal submanifolds of codimension greater than one in irreducible symmetric spaces of compact type occur as principal orbits of Hermann actions. However, we investigate the flows conceptionally without use of this fact. Concretely the investigation is performed by investigating the mean curvature flows having the lifts of the submanifolds to an (infinite deiminsional separable) Hilbert space through a Riemannian submersion as initial data.

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