Einstein metrics on aligned homogeneous spaces with two factors
Differential Geometry
2025-02-20 v2
Abstract
Given two homogeneous spaces of the form G_1/K and G_2/K, where G_1 and G_2 are compact simple Lie groups, we study the existence problem for G_1xG_2-invariant Einstein metrics on the homogeneous space M=G_1xG_2/K. For the large subclass C of spaces having three pairwise inequivalent isotropy irreducible summands (12 infinite families and 70 sporadic examples), we obtain that existence is equivalent to the existence of a real root for certain quartic polynomial depending on the dimensions and two Killing constants, which allows a full classification and the possibility to weigh the existence and non-existence pieces of C.
Keywords
Cite
@article{arxiv.2408.00456,
title = {Einstein metrics on aligned homogeneous spaces with two factors},
author = {Jorge Lauret and Cynthia Will},
journal= {arXiv preprint arXiv:2408.00456},
year = {2025}
}
Comments
23 pages, 5 figures. Final version accepted in J. London Math. Soc