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.
"Collapse of the mean curvature flow for isoparametric submanifolds in non-compact symmetric spaces." Kodai Math. J. 37 (2) 355 - 382, June 2014. https://doi.org/10.2996/kmj/1404393892