Rigidity of Homogeneous Gradient Soliton Metrics and Related Equations
Differential Geometry
2022-03-21 v2
Abstract
We prove structure results for homogeneous spaces that support a non-constant solution to two general classes of equations involving the Hessian of a function and an invariant 2-tensor. We also consider trace-free versions of these systems. Our results generalize earlier rigidity results for gradient Ricci solitons and warped product Einstein metrics. In particular, our results apply to homogeneous gradient solitons of any invariant curvature flow and give a new structure result for homogeneous conformally Einstein metrics.
Keywords
Cite
@article{arxiv.2007.11058,
title = {Rigidity of Homogeneous Gradient Soliton Metrics and Related Equations},
author = {Peter Petersen and William Wylie},
journal= {arXiv preprint arXiv:2007.11058},
year = {2022}
}
Comments
33 pages, v2. Added a rigidity statement to Thm 1.5 in the Codazzi case, Added an appendix on related work in the Kaehler case, added a number of references