On Biconservative Lorentz Hypersurface with non-diagonalizable shape operator

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.

References in corpus (1)

• Lorentz Hypersurfaces satisfying $△\vec{H}=\alpha \vec{H}$ with non diagonal shape operator

Cited by in corpus (2)

• Biconservative ideal hypersurfaces in Euclidean spaces
• Biharmonic $δ(\lowercase{r})$-ideal hypersurfaces in Euclidean spaces are minimal