A potential generalization of some canonical Riemannian metrics
Differential Geometry
2019-05-27 v1
Abstract
The aim of this paper is to study new classes of Riemannian manifolds endowed with a smooth potential function, including in a general framework classical canonical structures such as Einstein, harmonic curvature and Yamabe metrics, and, above all, gradient Ricci solitons. For the most rigid cases we give a complete classification, while for the others we provide rigidity and obstruction results, characterizations and nontrivial examples. In the final part of the paper we also describe the "nongradient" version of this construction.
Keywords
Cite
@article{arxiv.1705.10599,
title = {A potential generalization of some canonical Riemannian metrics},
author = {Giovanni Catino and Paolo Mastrolia},
journal= {arXiv preprint arXiv:1705.10599},
year = {2019}
}