The aim of this paper is to continue the geometric-analytic study of φ-curvatures initiated in [2]. These curvatures arise naturally in many geometric contexts, notably in Ricci-harmonic solitons theory. In the present paper we prove two rigidity results related to harmonic-Einstein manifolds, a generalization of the notion of Einstein manifolds to the present situation. We observe that, when we restrict our theorems to the classical case of Einstein manifolds, we obtain some new results even in this setting.

Marini, L., Rigoli, M. (2020). On the geometry of φ-curvatures. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 483(2) [10.1016/j.jmaa.2019.123657].

On the geometry of φ-curvatures

Marini L.
;
Rigoli M.
2020

Abstract

The aim of this paper is to continue the geometric-analytic study of φ-curvatures initiated in [2]. These curvatures arise naturally in many geometric contexts, notably in Ricci-harmonic solitons theory. In the present paper we prove two rigidity results related to harmonic-Einstein manifolds, a generalization of the notion of Einstein manifolds to the present situation. We observe that, when we restrict our theorems to the classical case of Einstein manifolds, we obtain some new results even in this setting.
Articolo in rivista - Articolo scientifico
Bochner-type equations; Harmonic-Einstein manifolds; Manifolds of constant sectional curvature; Poincaré-Sobolev inequalities; Stochastic completeness; φ-curvatures
English
2020
483
2
123657
none
Marini, L., Rigoli, M. (2020). On the geometry of φ-curvatures. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 483(2) [10.1016/j.jmaa.2019.123657].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/261066
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