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Scalar curvature rigidity of domains in a warped product

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arxiv 2407.10212 v1 pith:CB5ZCEIH submitted 2024-07-14 math.DG

Xiaoxiang Chai (POSTECH) , Xueyuan Wan (CQUT) This is my paper · ORCID
classification math.DG
keywords productrigiditywarpedcurvaturedomainsmetricscalarable
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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.

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  1. Gap phenomenon for scalar curvature

    math.DG 2025-01 conditional novelty 6.0 of 10

    Scalar curvature on any closed even-dimensional manifold with nonzero Euler characteristic can be increased by at most an explicit constant, the gap, which is a function of the minimal eigenvalue of the curvature oper...

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