Some classifications of biharmonic Lorentzian hypersurfaces in Minkowski 5-space $\mathbb E^5_1$

TL;DR

This paper classifies certain Lorentzian hypersurfaces in Minkowski 5-space with specific shape operator properties, proving they are biharmonic if and only if they are minimal, thus linking biharmonicity to minimality in these cases.

Contribution

It provides a classification of biharmonic Lorentzian hypersurfaces with non-diagonalizable shape operators in Minkowski 5-space, establishing their minimality as a necessary and sufficient condition.

Findings

Biharmonic Lorentzian hypersurfaces with specified shape operators are minimal.

Characterization of hypersurfaces with characteristic polynomial $(t-k_1)^2(t-k_3)(t-k_4)$ or $(t-k_1)^3(t-k_4)$.

Biharmonicity coincides with minimality in these cases.

Abstract

In this paper, we study Lorentzian hypersurfaces in Minkowski 5-space with non-diagonalizable shape operator whose characteristic polinomial is $(t-k_1)^2(t-k_3)(t-k_4)$ or $(t-k_1)^3(t-k_4)$. We proved that in these cases, a hypersurface is biharmonic if and only if it is minimal.