BICONSERVATIVE PNMCV SURFACES IN THE ARBITRARY DIMENSIONAL MINKOWSKI SPACE

Abstract

In this article, we study biconservative surfaces with parallel normalized mean curvature vector field in the arbitrary dimensional Minkowski space E m 1 , where m >= 4. Firstly, we obtain some geometric properties of these surfaces. In particular, we prove that if M is a PNMCV biconservative surface in E m 1 , then it must be contained in a 4-dimensional non-degenerated totally geodesic of E m 1 and all its shape operators are diagonalizable. Then, we give local classification theorems for biconservative PNMCV space-like and time-like surfaces in E 4 1 .