Kodai Mathematical Journal

Collapse of the mean curvature flow for isoparametric submanifolds in non-compact symmetric spaces

Naoyuki Koike

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Abstract

It is known that principal orbits of Hermann actions on a symmetric space of non-compact type are curvature-adapted isoparametric submanifolds having no focal point of non-Euclidean type on the ideal boundary of the ambient symmetric space. In this paper, we investigate the mean curvature flows for such a curvature-adapted isoparametric submanifold and its focal submanifold. Concretely the investigation is performed by investigating the mean curvature flows for the lift of the submanifold to an infinite dimensional pseudo-Hilbert space through a pseudo-Riemannian submersion.

Article information

Source
Kodai Math. J., Volume 37, Number 2 (2014), 355-382.

Dates
First available in Project Euclid: 3 July 2014

Permanent link to this document
https://projecteuclid.org/euclid.kmj/1404393892

Digital Object Identifier
doi:10.2996/kmj/1404393892

Mathematical Reviews number (MathSciNet)
MR3229081

Zentralblatt MATH identifier
1296.53130

Citation

Koike, Naoyuki. Collapse of the mean curvature flow for isoparametric submanifolds in non-compact symmetric spaces. Kodai Math. J. 37 (2014), no. 2, 355--382. doi:10.2996/kmj/1404393892. https://projecteuclid.org/euclid.kmj/1404393892


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