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.
A potential generalization of some canonical Riemannian metrics / G. Catino, P. Mastrolia. - In: ANNALS OF GLOBAL ANALYSIS AND GEOMETRY. - ISSN 0232-704X. - 55:4(2019 Jun), pp. 719-748. [10.1007/s10455-019-09649-w]
A potential generalization of some canonical Riemannian metrics
P. Mastrolia
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.
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