Comptes Rendus
Differential Geometry
Para-Kähler Einstein metrics on homogeneous manifolds
[Metriques para-Kähler Einstein sur des variétés homogènes]
Comptes Rendus. Mathématique, Volume 347 (2009) no. 1-2, pp. 69-72.

Une structure para-Kählérienne sur une variété M est la donnée d'un paire (g,K), où g est une metrique pseudo-riemannienne et K est un champ parallel d'endomorphismes anti-symétriques qui satisfait K2=Id. On donne une description de toutes les structures para-Kählériennes invariantes (g,K) sur des variétés homogènes M=G/H, où G est un group de Lie semisimple.

A para-Kähler structure on a manifold M is a pair (g,K) where g is a pseudo-Riemannian metric and K is a parallel field of skew-symmetric endomorphisms with K2=Id. We give a description of all invariant para-Kähler structures (g,K) on homogeneous manifolds M=G/H of semisimple Lie groups G.

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DOI : 10.1016/j.crma.2008.11.016

Dimitri V. Alekseevsky 1 ; Costantino Medori 2 ; Adriano Tomassini 2

1 The University of Edinburgh, James Clerk Maxwell Building, The King's Buildings, Mayfield Road, Edinburgh, EH9 3JZ, UK
2 Dipartimento di Matematica, Università di Parma, Viale G.P. Usberti, 53/A, 43100 Parma, Italy
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Dimitri V. Alekseevsky; Costantino Medori; Adriano Tomassini. Para-Kähler Einstein metrics on homogeneous manifolds. Comptes Rendus. Mathématique, Volume 347 (2009) no. 1-2, pp. 69-72. doi : 10.1016/j.crma.2008.11.016. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2008.11.016/

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This work was partially supported by Leverhulme Trust, EM/9/2005/0069, by the MIUR Project “Geometric Properties of Real and Complex Manifolds” and by GNSAGA of INdAM.

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