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Abstract: In this paper, we investigate the mean curvature flows for an equifocalsubmanifold in a symmetric space of compact type and its focal submanifolds asinitial data. It is known that equifocal submanifolds of codimension greaterthan one in irreducible symmetric spaces of compact type occur as principalorbits of Hermann actions. However, we investigate the flows conceptionallywithout use of this fact. Concretely the investigation is performed byinvestigating the mean curvature flows having the lifts of the submanifolds toan infinite deiminsional separable Hilbert space through a Riemanniansubmersion as initial data.



Author: Naoyuki Koike

Source: https://arxiv.org/







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