Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

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

Bouazza Kacimi, Ahmed Mohammed Cherif, Mustafa Özkan

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}.

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

Abstract

In this paper, we investigate the classification of -tensional hypersurfaces in a -dimensional space form of constant sectional curvature . Our results show that minimal hypersurfaces are the only -tensional hypersurfaces in -dimensional space forms, thereby providing an affirmative partial answer to Conjecture 3 proposed in \cite{kacimi}.
Paper Structure (2 sections, 2 theorems, 35 equations)

This paper contains 2 sections, 2 theorems, 35 equations.

Table of Contents

  1. Introduction
  2. $H$-tensional hypersurfaces in 4-dimensional space forms

Key Result

Theorem 2.1

A hypersurface $\iota: M^{m} \longrightarrow N^{m+1}(c)$ in a space of constant sectional curvature $c$ with mean curvature vector $H = \alpha e_{m+1}$ is $H$-tensional if and only if where $A$ denotes the Weingarten operator and $\Delta \alpha$ is the Laplacian of $\alpha$.

Theorems & Definitions (3)

  • Theorem 2.1
  • Theorem 2.2
  • proof