A potential generalization of some canonical Riemannian metrics

created by catino on 30 May 2017
modified on 24 May 2019

[BibTeX]

Published Paper

Inserted: 30 may 2017
Last Updated: 24 may 2019

Journal: Ann. Glob. Anal. Geom.
Volume: 55
Number: 4
Pages: 719-748
Year: 2019

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.