scholarly journals Critical metrics of the total scalar curvature functional on 4-manifolds

2015 ◽  
Vol 288 (16) ◽  
pp. 1814-1821 ◽  
Author(s):  
A. Barros ◽  
B. Leandro ◽  
E. Ribeiro
Keyword(s):  
Scalar Curvature ◽  
Critical Metrics ◽  
Total Scalar Curvature ◽  
Scalar Curvature Functional

scholarly journals On static manifolds and related critical spaces with cyclic parallel Ricci tensor

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
H. Baltazar ◽  
A. Da Silva
Keyword(s):  
Scalar Curvature ◽  
Ricci Tensor ◽  
Critical Spaces ◽  
3 Dimensional ◽  
Critical Metrics ◽  
Volume Functional ◽  
Total Scalar Curvature ◽  
Cyclic Parallel Ricci Tensor ◽  
Scalar Curvature Functional ◽  
Parallel Ricci Tensor

Abstract We classify 3-dimensional compact Riemannian manifolds (M 3, g) that admit a non-constant solution to the equation −Δfg +Hess f − f Ric = μ Ric +λg for some special constants (μ, λ), under the assumption that the manifold has cyclic parallel Ricci tensor. Namely, the structures that we study here are: positive static triples, critical metrics of the volume functional, and critical metrics of the total scalar curvature functional. We also classify n-dimensional critical metrics of the volume functional with non-positive scalar curvature and satisfying the cyclic parallel Ricci tensor condition.

scholarly journals ON UNIQUENESS AND DIFFERENTIABILITY IN THE SPACE OF YAMABE METRICS

2005 ◽  
Vol 07 (03) ◽  
pp. 299-310 ◽  
Author(s):  
MICHAEL T. ANDERSON
Keyword(s):  
Scalar Curvature ◽  
Sufficient Conditions ◽  
Locally Maximal ◽  
Generic Set ◽  
Scalar Curvature Functional

It is shown that there is a unique Yamabe representative for a generic set of conformal classes in the space of metrics on any manifold. At such classes, the scalar curvature functional is shown to be differentiable on the space of Yamabe metrics. In addition, some sufficient conditions are given which imply that a Yamabe metric of locally maximal scalar curvature is necessarily Einstein.

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