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arXiv · 1504.01498

Metrics with Prescribed Ricci Curvature on Homogeneous Spaces

Artem Pulemotov
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Abstract

Let $G$ be a compact connected Lie group and $H$ a closed subgroup of $G$. Suppose the homogeneous space $G/H$ is effective and has dimension 3 or higher. Consider a $G$-invariant, symmetric, positive-semidefinite, nonzero (0,2)-tensor field $T$ on $G/H$. Assume that $H$ is a maximal connected Lie subgroup of $G$. We prove the existence of a $G$-invariant Riemannian metric $g$ and a positive number $c$ such that the Ricci curvature of $g$ coincides with $cT$ on $G/H$. Afterwards, we examine what happens when the maximality hypothesis fails to hold.

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Artem Pulemotov. 2015-04-07. Metrics with Prescribed Ricci Curvature on Homogeneous Spaces. https://doi.org/10.1016/j.geomphys.2016.04.003

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