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 , this problem asks for solutions to the equation for some constant . 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.
Keywords
Cite
@article{arxiv.2110.14129,
title = {On the variational properties of the prescribed Ricci curvature functional},
author = {Artem Pulemotov and Wolfgang Ziller},
journal= {arXiv preprint arXiv:2110.14129},
year = {2023}
}
Comments
24 pages, 3 figures. Version 2: A portion of this paper has been generalised and moved to the new paper "Palais-Smale sequences for the prescribed Ricci curvature functional"; the current version deals with the question of when the prescribed Ricci curvature functional assumes its maximum