A classification of Biconservative Hypersurfaces in the Minkowski spaces

TL;DR

This paper proves that Lorentzian biconservative hypersurfaces with lightlike mean curvature gradient do not exist in Minkowski spaces through detailed geometric analysis.

Contribution

It provides a non-existence result for a specific class of biconservative hypersurfaces in Minkowski spaces, expanding understanding of their geometric properties.

Findings

Non-existence of Lorentzian biconservative hypersurfaces with lightlike mean curvature gradient in Minkowski spaces

Rigorous analysis of Codazzi and Gauss equations used in the proof

Clarifies geometric constraints of hypersurfaces in Lorentzian geometry

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.