scholarly journals Maxima of Curvature Functionals and the Prescribed Ricci Curvature Problem on Homogeneous Spaces

2019 ◽  
Vol 30 (1) ◽  
pp. 987-1010 ◽  
Author(s):  
Artem Pulemotov
Keyword(s):  
Ricci Curvature ◽  
Homogeneous Spaces ◽  
Curvature Functionals ◽  
Curvature Problem

scholarly journals Prescribing Ricci curvature on homogeneous spaces

2022 ◽  
Vol 0 (0) ◽  
Author(s):  
Jorge Lauret ◽  
Cynthia E. Will
Keyword(s):  
Homogeneous Space ◽  
Ricci Curvature ◽  
Homogeneous Spaces ◽  
Main Tool ◽  
Moment Map ◽  
Invariant Metrics ◽  
Variety Of Algebras ◽  
Compact Case ◽  
The Moment ◽  
Curvature Problem

Abstract The prescribed Ricci curvature problem in the context of G-invariant metrics on a homogeneous space M = G / K {M=G/K} is studied. We focus on the metrics at which the map g ↦ Rc ⁡ ( g ) {g\mapsto\operatorname{Rc}(g)} is, locally, as injective and surjective as it can be. Our main result is that such property is generic in the compact case. Our main tool is a formula for the Lichnerowicz Laplacian we prove in terms of the moment map for the variety of algebras.

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