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

Artem Pulemotov

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arXiv · 1808.10798

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

Artem Pulemotov

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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.

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BibTeX RIS

Artem Pulemotov. 2018-08-31. Maxima of Curvature Functionals and the Prescribed Ricci Curvature Problem on Homogeneous Spaces. https://arxiv.org/abs/1808.10798

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