Homogeneous almost-Kähler manifolds and the Chern–Einstein equation

  • Dmitri V. Alekseevsky
  • Fabio PodestàEmail author


Given a non-compact semisimple Lie group G we describe all homogeneous spaces G / L carrying an invariant almost-Kähler structure \((\omega ,J)\). When L is abelian and G is of classical type, we classify all such spaces which are Chern–Einstein, i.e. which satisfy \(\rho = \lambda \omega \) for some \(\lambda \in {\mathbb {R}}\), where \(\rho \) is the Ricci form associated to the Chern connection.


Symplectic manifolds Homogeneous spaces Chern Ricci form 

Mathematics Subject Classification

53C25 53C30 



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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Institute for Information Transmission Problem RASMoscowRussia
  2. 2.Faculty of ScienceUniversity of Hradec KraloveHradec KrálovéCzech Republic
  3. 3.Dipartimento di Matematica e Informatica “Ulisse Dini”Università di FirenzeFlorenceItaly

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