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

Abstract

Consider a compact Lie group $G$ and a closed Lie subgroup $H<G$. Let $\mathcal{M}$ be the set of $G$-invariant Riemannian metrics on the homogeneous space $M=G/H$. By studying variational properties of the scalar curvature functional on $\mathcal{M}$, we obtain an existence theorem for solutions to the prescribed Ricci curvature problem on $M$. To illustrate the applicability of this result, we explore cases where $M$ is a generalised Wallach space and a generalised flag manifold.

arXiv comment17 pages

References in corpus (4)

• Metrics with Prescribed Ricci Curvature on Homogeneous Spaces
• The Prescribed Ricci Curvature Problem on Homogeneous Spaces with Intermediate Subgroups
• Geodesics in generalized Wallach spaces
• Inversion of some curvature operators near a parallel Ricci metric II: Non-compact manifold with bounded geometry

Cited by in corpus (1)

• On the Ricci iteration for homogeneous metrics on spheres and projective spaces