Einstein metrics on aligned homogeneous spaces with two factors

Jorge Lauret; Cynthia Will

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arXiv · 2408.00456

Einstein metrics on aligned homogeneous spaces with two factors

Jorge Lauret·Cynthia Will

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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.

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BibTeX RIS

Jorge Lauret, Cynthia Will. 2024-08-01. Einstein metrics on aligned homogeneous spaces with two factors. https://arxiv.org/abs/2408.00456

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