On the variational properties of the prescribed Ricci curvature functional
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.
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