$H$-tensional hypersurfaces in $4$-dimensional space forms

TL;DR

This paper classifies $H$-tensional hypersurfaces in 4-dimensional space forms, concluding that only minimal hypersurfaces satisfy this condition, thus supporting a specific conjecture in the field.

Contribution

It proves that in 4-dimensional space forms, the only $H$-tensional hypersurfaces are minimal, providing a partial confirmation of an existing conjecture.

Findings

Minimal hypersurfaces are the only $H$-tensional hypersurfaces in 4D space forms.

Supports Conjecture 3 from previous literature.

Advances understanding of hypersurface classification in constant curvature spaces.

Abstract

In this paper, we investigate the classification of $H$-tensional hypersurfaces $M$ in a $4$-dimensional space form $N^4(c)$ of constant sectional curvature $c$. Our results show that minimal hypersurfaces are the only $H$-tensional hypersurfaces in $4$-dimensional space forms, thereby providing an affirmative partial answer to Conjecture 3 proposed in \cite{kacimi}.