PreprintCC BY 4.0arXiv
Rigidity of Constant-Scalar-Curvature Ricci Shrinkers with Totally Geodesic Focal Set
Abstract
Let (Mn,g,f) be a complete connected shrinking gradient Ricci soliton with constant scalar curvature, satisfying Ric+∇2f=1/2g. 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.
Related
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BibTeX
@misc{li2026rigidity,
title = {{Rigidity of Constant-Scalar-Curvature Ricci Shrinkers with Totally Geodesic Focal Set}},
author = {Fengjiang Li and Wenqi Li and Jianyu Ou and Yuanyuan Qu and Guoqiang Wu and Detang Zhou},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.37151},
eprint = {2610.37151},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.37151},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Rigidity of Constant-Scalar-Curvature Ricci Shrinkers with Totally Geodesic Focal Set
AU - Fengjiang Li
AU - Wenqi Li
AU - Jianyu Ou
AU - Yuanyuan Qu
AU - Guoqiang Wu
AU - Detang Zhou
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.37151
UR - https://arxiv.org/abs/2610.37151
AB - Let (M^n,g,f) be a complete connected shrinking gradient Ricci soliton with constant scalar curvature, satisfying Ric+∇^2f=1/2g. 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.
ER -