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.
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