On Horospherical Rigidity

Abstract We prove that on a closed negatively curved manifold of dimension greater than two, a horosphere endowed with the induced Riemannian metric cannot have non-negative scalar curvature unless the manifold is real hyperbolic, in which case all horospheres are flat.

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Publication Details

Journal
International Mathematics Research Notices
Published
2025-08-25
DOI
https://doi.org/10.1093/imrn/rnaf267
Primary Topic
Geochemistry and Geologic Mapping
Type
article
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article

On Horospherical Rigidity

International Mathematics Research Notices
Geochemistry and Geologic Mapping
article

On Horospherical Rigidity

article en

Abstract

Abstract We prove that on a closed negatively curved manifold of dimension greater than two, a horosphere endowed with the induced Riemannian metric cannot have non-negative scalar curvature unless the manifold is real hyperbolic, in which case all horospheres are flat.

International Mathematics Research NoticesVol. 2025(18)
University of Georgia (US), Institut de Mathématiques de Jussieu-Paris Rive Gauche (FR), Sorbonne Université (FR), Institut Fourier (FR), Université Grenoble Alpes (FR)
Reduced inequalities
Openalex Percentile: Top 34%
Geochemistry and Geologic Mapping
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