A para-Kähler structure on a manifold M is a pair where g is a pseudo-Riemannian metric and K is a parallel field of skew-symmetric endomorphisms with . We give a description of all invariant para-Kähler structures on homogeneous manifolds of semisimple Lie groups G.
Une structure para-Kählérienne sur une variété M est la donnée d'un paire , où g est une metrique pseudo-riemannienne et K est un champ parallel d'endomorphismes anti-symétriques qui satisfait . On donne une description de toutes les structures para-Kählériennes invariantes sur des variétés homogènes , où G est un group de Lie semisimple.
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@article{CRMATH_2009__347_1-2_69_0, author = {Alekseevsky, Dimitri V. and Medori, Costantino and Tomassini, Adriano}, title = {Para-K\"ahler {Einstein} metrics on homogeneous manifolds}, journal = {Comptes Rendus. Math\'ematique}, pages = {69--72}, publisher = {Elsevier}, volume = {347}, number = {1-2}, year = {2009}, doi = {10.1016/j.crma.2008.11.016}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.crma.2008.11.016/} }
TY - JOUR AU - Alekseevsky, Dimitri V. AU - Medori, Costantino AU - Tomassini, Adriano TI - Para-Kähler Einstein metrics on homogeneous manifolds JO - Comptes Rendus. Mathématique PY - 2009 SP - 69 EP - 72 VL - 347 IS - 1-2 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2008.11.016/ DO - 10.1016/j.crma.2008.11.016 LA - en ID - CRMATH_2009__347_1-2_69_0 ER -
%0 Journal Article %A Alekseevsky, Dimitri V. %A Medori, Costantino %A Tomassini, Adriano %T Para-Kähler Einstein metrics on homogeneous manifolds %J Comptes Rendus. Mathématique %D 2009 %P 69-72 %V 347 %N 1-2 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2008.11.016/ %R 10.1016/j.crma.2008.11.016 %G en %F CRMATH_2009__347_1-2_69_0
Alekseevsky, Dimitri V.; Medori, Costantino; Tomassini, Adriano. 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. http://www.numdam.org/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.