A Classification of Biconservative Hypersurfaces in a Pseudo-Euclidean Space

TL;DR

This paper classifies biconservative hypersurfaces with specific curvature properties in a pseudo-Euclidean space, providing a complete classification for certain cases and explicit examples for others.

Contribution

It offers a complete classification of biconservative hypersurfaces with three principal curvatures and explicit examples with four principal curvatures in a pseudo-Euclidean space.

Findings

Classified biconservative hypersurfaces with three principal curvatures

Provided explicit example with four principal curvatures

Enhanced understanding of hypersurface geometry in pseudo-Euclidean spaces

Abstract

In this paper, we study biconservative hypersurfaces of index 2 in $\mathbb E^{5}_{2}$. We give the complete classification of biconservative hypersurfaces with diagonalizable shape operator at exactly three distinct principal curvatures. We also give an explicit example of biconservative hypersurfaces with four distinct principal curvatures.