Annals of Global Analysis and Geometry

, Volume 55, Issue 4, pp 719–748 | Cite as

A potential generalization of some canonical Riemannian metrics

  • Giovanni Catino
  • Paolo MastroliaEmail author


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.


Canonical metrics Einstein metrics Harmonic curvature Yamabe metrics Ricci solitons 

Mathematics Subject Classification

53C20 53C25 



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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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Dipartimento di MatematicaPolitecnico di MilanoMilanItaly
  2. 2.Dipartimento di MatematicaUniversità degli Studi di MilanoMilanItaly

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