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A potential generalization of some canonical Riemannian metrics

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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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Acknowledgements

The authors are members of the Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM) and they are partially supported by GNAMPA project “Strutture di tipo Einstein e Analisi Geometrica su varietà Riemanniane e Lorentziane.”

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  1. Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133, Milan, Italy

    Giovanni Catino

  2. Dipartimento di Matematica, Università degli Studi di Milano, Via Saldini 50, 20133, Milan, Italy

    Paolo Mastrolia

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  1. Giovanni Catino
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Correspondence to Paolo Mastrolia.

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Catino, G., Mastrolia, P. A potential generalization of some canonical Riemannian metrics. Ann Glob Anal Geom 55, 719–748 (2019). https://doi.org/10.1007/s10455-019-09649-w

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