On Biconservative Lorentz Hypersurface with non-diagonalizable shape operator

TL;DR

This paper studies biconservative Lorentz hypersurfaces in pseudo-Euclidean space with complex eigenvalues, establishing conditions for constant mean curvature and analyzing cases with multiple principal curvatures.

Contribution

It characterizes biconservative Lorentz hypersurfaces with complex eigenvalues, proving constant mean curvature under certain eigenvalue multiplicity conditions and examining specific curvature cases.

Findings

Hypersurfaces with up to five principal curvatures have constant mean curvature.

Analysis of hypersurfaces with six principal curvatures and constant second fundamental form length.

Abstract

In this paper, we obtain some properties of biconservative Lorentz hypersurface $M_{1}^{n}$ in $E_{1}^{n+1}$ having shape operator with complex eigen values. We prove that every biconservative Lorentz hypersurface $M_{1}^{n}$ in $E_{1}^{n+1}$ whose shape operator has complex eigen values with at most five distinct principal curvatures has constant mean curvature. Also, we investigate such type of hypersurface with constant length of second fundamental form having six distinct principal curvatures.