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arXiv · 2110.14129

On the variational properties of the prescribed Ricci curvature functional

Artem Pulemotov·Wolfgang Ziller
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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 $\mathrm{Ric}(g)=cT$ 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.

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Artem Pulemotov, Wolfgang Ziller. 2021-10-27. On the variational properties of the prescribed Ricci curvature functional. https://arxiv.org/abs/2110.14129

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