# A potential generalization of some canonical Riemannian metrics

created by catino on 30 May 2017
modified on 30 Dec 2018

[BibTeX]

Accepted Paper

Inserted: 30 may 2017
Last Updated: 30 dec 2018

Journal: Ann. Glob. Anal. Geom.
Year: 2018

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.