Calculus of Variations and Geometric Measure Theory
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G. Catino - P. Mastrolia

A potential generalization of some canonical Riemannian metrics

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


Accepted Paper

Inserted: 30 may 2017
Last Updated: 30 dec 2018

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


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.


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