Existence of homogeneous metrics with prescribed Ricci curvature
Mark Gould1; Artem Pulemotov1
1 School of Mathematics and Physics The University of Queensland St Lucia, QLD 4072 (Australia)
Séminaire de théorie spectrale et géométrie, Volume 33 (2015-2016), pp. 47-54.

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.

Published online:
DOI: 10.5802/tsg.313
Mark Gould 1; Artem Pulemotov 1

1 School of Mathematics and Physics The University of Queensland St Lucia, QLD 4072 (Australia) 
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Mark Gould; Artem Pulemotov. Existence of homogeneous metrics with prescribed Ricci curvature. Séminaire de théorie spectrale et géométrie, Volume 33 (2015-2016), pp. 47-54. doi : 10.5802/tsg.313. https://proceedings.centre-mersenne.org/articles/10.5802/tsg.313/

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