Rigidity theorem for a static triple with half harmonic Weyl curvature

TL;DR

This paper proves that static triples with half harmonic Weyl curvature and positive scalar curvature are uniquely characterized as the standard hemisphere, establishing a rigidity result in geometric analysis.

Contribution

It establishes a rigidity theorem for static triples with specific curvature conditions, identifying the standard hemisphere as the only such example.

Findings

Static triples with half harmonic Weyl curvature and positive scalar curvature are the standard hemisphere.

The result characterizes the geometric structure under the given curvature conditions.

Provides a uniqueness result in the classification of static triples.

Abstract

In this paper, we prove that the static triple with half harmonic Weyl curvature and positive scalar curvature must be the standard hemisphere.