Work

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

Year: 2026

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.37151

Authors: Li, Fengjiang, Li, Wenqi, Ou, Jianyu, Qu, Yuanyuan, Wu, Guoqiang, Zhou, Detang

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7224078219

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