Collapse of the mean curvature flow for proper complex equifocal submanifolds

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

2010-01-20

arxiv.org/abs/1001.3508v4

Mathematics

Differential Geometry

30pages

Scientific paper

It is known that principal orbits of Hermann type action on a symmetric space of non-compact type are proper complex equifocal and curvature-adapted and, conversely, irreducible curvature-adapted proper complex equifocal submanifolds of codimension greater than one in the symmetric space occur as principal orbits of Hermann type actions. In this paper, we investigate the mean curvature flows having a curvature-adapted proper complex equifocal submanifold or its focal submanifold as initial data conceptionally without use of the second part of the above facts. Concretely the investigation is performed by investigating the mean curvature flows for the lift of the submanifold to an infinite dimensonal pseudo-Hilbert space through a pseudo-Riemannian submersion.

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