A potential generalization of some canonical Riemannian metrics

被引：2
作者：
Catino, Giovanni [1 ]
Mastrolia, Paolo [2 ]
机构：
[1] Politecn Milan, Dipartimento Matemat, Piazza Leonardo da Vinci 32, I-20133 Milan, Italy
[2] Univ Milan, Dipartimento Matemat, Via Saldini 50, I-20133 Milan, Italy
来源：
ANNALS OF GLOBAL ANALYSIS AND GEOMETRY | 2019年 / 55卷 / 04期
关键词：
Canonical metrics; Einstein metrics; Harmonic curvature; Yamabe metrics; Ricci solitons; MANIFOLDS; CURVATURE; SOLITONS;
D O I：
10.1007/s10455-019-09649-w
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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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页码：719 / 748
页数：30
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