Geometry of position functions of Riemannian submanifolds in pseudo-Euclidean space

Abstract

It is well-known that the position function is the simplest and the most natural geometric object associated with a submanifold in a Euclidean space or, more generally, in a pseudo-Euclidean space. We call a submanifold T-constant (respectively, N-constant) if the tangential component (respectively, the normal component) of its position function has constant length. The main purpose of this paper is to classify space-like submanifolds in pseudo-Euclidean space which are either T-constant or N-constant.