A Classification of Parallel Normalized Biconservative Submanifold in the Minkowski Space in Arbitrary Dimension

Abstract

IIn this paper, we examine PNMCV-MCGL biconservative submanifold in a Minkowski space $\mathbb{E}_1^{n+2}$ with nondiagonalizable shape operator, where PNMCV-MCGL submanifold denotes a submanifold with parallel normalized mean curvature vector and the mean curvature whose gradient is lightlike ($\langle\nabla H,\nabla H\rangle=0$). We obtain some conditions about connection forms, principal curvatures and some results about them. Then we use them to obtain a classification of such submanifolds. Finally, we showed that there is no biconservative such submanifold in Minkowski space of arbitrary dimension.