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Prescribing Ricci curvature on homogeneous spaces

  • Jorge Lauret EMAIL logo und Cynthia E. Will
Veröffentlicht/Copyright: 6. Januar 2022

Abstract

The prescribed Ricci curvature problem in the context of G-invariant metrics on a homogeneous space M=G/K is studied. We focus on the metrics at which the map gRc(g) is, locally, as injective and surjective as it can be. Our main result is that such property is generic in the compact case. Our main tool is a formula for the Lichnerowicz Laplacian we prove in terms of the moment map for the variety of algebras.

Funding statement: This research was partially supported by a grant from Universidad Nacional de Córdoba (Argentina).

Acknowledgements

We are grateful with Marcos Salvai and the anonymous referee for very helpful comments.

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Received: 2020-10-23
Revised: 2021-09-28
Published Online: 2022-01-06
Published in Print: 2022-02-01

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