On the variational properties of the prescribed Ricci curvature functional

2021/10/27 by Artem Pulemotov, Wolfgang Ziller, Pulemotov, Artem +1 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2110.14129

openalex publication_date 2021/10/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the prescribed Ricci curvature problem for homogeneous metrics. Given a (0,2)-tensor field T, this problem asks for solutions to the equation Ric(g)=cT for some constant c. Our approach is based on examining global properties of the scalar curvature functional whose critical points are solutions to this equation. We produce conditions for a general homogeneous space under which it has a global maximum. Finally, we study the behavior of the functional in specific examples to illustrate our result.

Citations

• Diverging sequences of unit volume invariant metrics with bounded curvature

Cited by

• Homogeneous spaces with two equivalent isotropy summands develop positive Ricci curvature under Ricci flow

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