Scalar curvature rigidity of domains in a warped product

TL;DR

This paper establishes scalar curvature rigidity results for domains in warped product manifolds using a new Dirac operator approach, extending known rigidity theorems to more general settings including hyperbolic space.

Contribution

It introduces a novel connection on a twisted spinor bundle and applies it to prove scalar curvature rigidity in warped products and hyperbolic space.

Findings

Proves scalar curvature rigidity for domains in warped products.

Addresses Gromov dihedral rigidity in hyperbolic space with angle conditions.

Develops a new Dirac operator framework for these rigidity results.

Abstract

By exploiting the conformality of a warped product metric with a direct product metric, we develop a new connection on a twisted spinor bundle and its associated Dirac operator. We obtain a Llarull type scalar curvature rigidity for a general class of domains in a warped product. Also, we are able to address Gromov dihedral rigidity in hyperbolic space assuming matching angles.