Rigidity of Constant-Scalar-Curvature Ricci Shrinkers with Totally Geodesic Focal Set

Let $(M^n,g,f)$ be a complete connected shrinking gradient Ricci soliton with constant scalar curvature, satisfying \[ \Ric+\nabla^2f=\frac12g. \] We prove that if the focal set of $f$ is totally geodesic, then $M$ is rigid. Equivalently, its universal cover is a product of a compact Einstein manifold and a Euclidean space.

Authors

Publication Details

Journal
arXiv (Cornell University)
Published
2026-10-27
DOI
https://doi.org/10.48550/arxiv.2610.37151
Primary Topic
Geometric Analysis and Curvature Flows
Type
preprint
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preprint

Rigidity of Constant-Scalar-Curvature Ricci Shrinkers with Totally Geodesic Focal Set

周德堂, Yuanyuan Qu, Wenqi Li, Jianyu Ou et al.
arXiv (Cornell University)
Geometric Analysis and Curvature Flows
preprint

Rigidity of Constant-Scalar-Curvature Ricci Shrinkers with Totally Geodesic Focal Set

周德堂, Yuanyuan Qu, Wenqi Li, Jianyu Ou, Guoqiang Wu, Fengjiang Li
preprint en

Abstract

Let $(M^n,g,f)$ be a complete connected shrinking gradient Ricci soliton with constant scalar curvature, satisfying \[ \Ric+\nabla^2f=\frac12g. \] We prove that if the focal set of $f$ is totally geodesic, then $M$ is rigid. Equivalently, its universal cover is a product of a compact Einstein manifold and a Euclidean space.

arXiv (Cornell University)
Geometric Analysis and Curvature Flows
DOIOpen Access PDFOpenAlex
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Rigidity of Constant-Scalar-Curvature Ricci Shrinkers with Totally Geodesic Focal Set — 周德堂, Yuanyuan Qu, et al. · arXiv (Cornell University) (2026) | TGRS Research Map | TGRS