Spacelike self-similar shrinking solutions of the mean curvature flow in pseudo-Euclidean spaces

摘要

I classify spacelike self-similar shrinking solutions of the mean curvature flow in pseudo-Euclidean space in arbitrary codimension, if the mean curvature vector is not a null vector and the principal normal vector is parallel in the normal bundle. Moreover, I exclude the existence of such self-shrinkers in several cases. The classification is analogous to the existing classification in the Euclidean case [20, 27].