A classification of Biconservative Hypersurfaces in the Minkowski spaces

Abstract

In this paper, we study Lorentzian biconservative hypersurfaces for which the gradient of their mean curvature $H$ is lightlike, i.e. $\langle \gr H,\gr H\rangle=0$. We establish the non-existence of such hypersurfaces in the Minkowski spaces by conducting a rigorous analysis of both the Codazzi and Gauss equations.

This manuscript is not well written. So it is needed to be revised carefully. It is not suitable for scientific research with the current version