On steady and expanding Ricci solitons with asymptotic symmetries

Fuente: arXiv
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Main Author: Law, Michael B.
Format: Preprint
Published: 2025
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author Law, Michael B.
author_facet Law, Michael B.
contents We establish a symmetry principle for asymptotically cylindrical steady gradient Ricci solitons (GRSs) and asymptotically conical expanding GRSs with homogeneous links. Using this, we show that the Bryant steady soliton is the unique asymptotically cylindrical steady GRS that has a round spherical link and satisfies a particular quantitative rigidity condition. A similar characterization is proved for Bryant's expanding solitons. Finally, we establish a global symmetry result for GRSs which exhibit the aforementioned asymptotics with quotient-Berger sphere asymptotic links.
format Preprint
id arxiv_https___arxiv_org_abs_2505_20576
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle On steady and expanding Ricci solitons with asymptotic symmetries
Law, Michael B.
Differential Geometry
We establish a symmetry principle for asymptotically cylindrical steady gradient Ricci solitons (GRSs) and asymptotically conical expanding GRSs with homogeneous links. Using this, we show that the Bryant steady soliton is the unique asymptotically cylindrical steady GRS that has a round spherical link and satisfies a particular quantitative rigidity condition. A similar characterization is proved for Bryant's expanding solitons. Finally, we establish a global symmetry result for GRSs which exhibit the aforementioned asymptotics with quotient-Berger sphere asymptotic links.
title On steady and expanding Ricci solitons with asymptotic symmetries
topic Differential Geometry
url https://arxiv.org/abs/2505.20576