The preservability of the curvature-adaptedness along the mean curvature flow

Abstract

In this paper, we investigate the preservability of the curvature-adaptedness along the mean curvature flow starting from a compact curvature-adapted hypersurface in locally symmetric spaces, where the curvature-adaptedness means that the shape operator and the normal Jacobi operator of the hypersurface commute.

arXiv comment19 pages, 1 figure