Existence of homogeneous metrics with prescribed Ricci curvature | Zendy

M. D. Gould | Zendy; Artem Pulemotov | Zendy

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Existence of homogeneous metrics with prescribed Ricci curvature

Author(s) -

M. D. Gould,

Artem Pulemotov

Publication year - 2018

Publication title -

séminaire de théorie spectrale et géométrie

Language(s) - English

Resource type - Journals

eISSN - 2118-9242

pISSN - 1624-5458

DOI - 10.5802/tsg.313

Subject(s) - mathematics , ricci curvature , lie group , pure mathematics , homogeneous , invariant (physics) , ricci decomposition , curvature , isotropy , riemann curvature tensor , ricci flow , mathematical analysis , metric (unit) , mathematical physics , combinatorics , geometry , physics , quantum mechanics , operations management , economics

— Consider a compact Lie group G and a closed subgroup H < G. Suppose T is a positive-definite G-invariant (0,2)-tensor field on the homogeneous space M = G/H. In this note, we state a sufficient condition for the existence of a G-invariant Riemannian metric on M whose Ricci curvature coincides with cT for some c > 0. This condition is, in fact, necessary if the isotropy representation of M splits into two inequivalent irreducible summands. After stating the main result, we work out an example.

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