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arXiv · 2610.37151

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

Fengjiang Li·Wenqi Li·Jianyu Ou·Yuanyuan Qu·Guoqiang Wu·Detang Zhou
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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.

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Fengjiang Li, Wenqi Li, Jianyu Ou, Yuanyuan Qu, Guoqiang Wu, Detang Zhou. 2026-10-27. Rigidity of Constant-Scalar-Curvature Ricci Shrinkers with Totally Geodesic Focal Set. https://arxiv.org/abs/2610.37151

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