Homogeneous almost-Kähler manifolds and the Chern–Einstein equation

Abstract

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.

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Correspondence to Fabio Podestà.

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Dmitri V. Alekseevsky was partially supported by grant no. 18-00496S of the Czech Science Foundation.

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Alekseevsky, D.V., Podestà, F. Homogeneous almost-Kähler manifolds and the Chern–Einstein equation. Math. Z. 296, 831–846 (2020). https://doi.org/10.1007/s00209-019-02446-y

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Keywords

  • Symplectic manifolds
  • Homogeneous spaces
  • Chern Ricci form

Mathematics Subject Classification

  • 53C25
  • 53C30