Spaces of Metrics and Curvature Functionals* *The author expresses his appreciation to Professors B.-Y. Chen, T. Draghici and O. Gil-Medrano for reading the first draft of this essay and giving many helpful comments.

2000 ◽  
pp. 153-185 ◽  
Author(s):  
David E. Blair
Keyword(s):  
Curvature Functionals ◽  
Spaces Of Metrics

scholarly journals Variational properties of quadratic curvature functionals

2018 ◽  
Vol 62 (9) ◽  
pp. 1765-1778
Author(s):  
Weimin Sheng ◽  
Lisheng Wang
Keyword(s):  
Curvature Functionals

Finite element minimization of curvature functionals with anisotropy

CALCOLO ◽  
1994 ◽  
Vol 31 (3-4) ◽  
pp. 191-210 ◽  
Author(s):  
F. Fierro ◽  
R. Goglione ◽  
M. Paolini
Keyword(s):  
Finite Element ◽  
Curvature Functionals

Critical metrics for all quadratic curvature functionals

2021 ◽  
Author(s):  
Miguel Brozos‐Vázquez ◽  
Sandro Caeiro‐Oliveira ◽  
Eduardo García‐Río
Keyword(s):  
Critical Metrics ◽  
Curvature Functionals

scholarly journals Rigidity and stability of Einstein metrics for quadratic curvature functionals

2015 ◽  
Vol 2015 (700) ◽  
Author(s):  
Matthew J. Gursky ◽  
Jeff A. Viaclovsky
Keyword(s):  
Critical Points ◽  
Moduli Space ◽  
Einstein Metrics ◽  
Riemannian Metrics ◽  
Local Minimizers ◽  
Lagrange Equations ◽  
Critical Metrics ◽  
Local Properties ◽  
Space Of Riemannian Metrics ◽  
Curvature Functionals

AbstractWe investigate rigidity and stability properties of critical points of quadratic curvature functionals on the space of Riemannian metrics. We show it is possible to “gauge” the Euler–Lagrange equations, in a self-adjoint fashion, to become elliptic. Fredholm theory may then be used to describe local properties of the moduli space of critical metrics. We show a number of compact examples are infinitesimally rigid, and consequently, are isolated critical points in the space of unit-volume Riemannian metrics. We then give examples of critical metrics which are strict local minimizers (up to diffeomorphism and scaling). A corollary is a local “reverse Bishop's inequality” for such metrics. In particular, any metric

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