On the geometry of φ-curvatures

被引：2
|
作者：
Marini, Ludovico [1 ]
Rigoli, Marco [1 ]
机构：
[1] Univ Milan, Dipartirnento Matemat, Via Saldini 50, I-20133 Milan, Italy
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2020年 / 483卷 / 02期
关键词：
phi-curvatures; Harmonic-Einstein manifolds; Manifolds of constant sectional curvature; Bochner-type equations; Stochastic completeness; Poincare-Sobolev inequalities;
D O I：
10.1016/j.jmaa.2019.123657
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The aim of this paper is to continue the geometric-analytic study of co-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. (C) 2019 Elsevier Inc. All rights reserved.
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页数：22
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