scholarly journals A note on critical point metrics of the total scalar curvature functional

2015 ◽  
Vol 424 (2) ◽  
pp. 1544-1548 ◽  
Author(s):  
Benedito Leandro Neto
Keyword(s):  
Scalar Curvature ◽  
Critical Point ◽  
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 CRITICAL POINT METRICS OF THE TOTAL SCALAR CURVATURE

2012 ◽  
Vol 49 (3) ◽  
pp. 655-667 ◽  
Author(s):  
Jeong-Wook Chang ◽  
Seung-Su Hwang ◽  
Gab-Jin Yun
Keyword(s):  
Scalar Curvature ◽  
Critical Point ◽  
Total Scalar Curvature
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