A spinorial approach to constant scalar curvature hypersurfaces in pseudo-hyperbolic manifolds

TL;DR

This paper employs spinorial methods to establish a Heintze-Karcher inequality and an Alexandrov type theorem for constant scalar curvature hypersurfaces in certain pseudo-hyperbolic manifolds, advancing geometric analysis in these spaces.

Contribution

It introduces a novel spinorial approach to derive geometric inequalities and classification results for hypersurfaces in pseudo-hyperbolic manifolds.

Findings

Proved a Heintze-Karcher type inequality in pseudo-hyperbolic spaces.

Established an Alexandrov type theorem for constant scalar curvature hypersurfaces.

Demonstrated the effectiveness of spinorial techniques in geometric inequalities.

Abstract

Using spinorial techniques, we prove, for a class of pseudo-hyperbolic ambient manifolds, a Heintze-Karcher type inequality. We then use this inequality to show an Alexandrov type theorem in such spaces.