Homogeneous almost K\"ahler manifolds and the Chern-Einstein equation

Dmitri V. Alekseevsky; Fabio Podestà

Homogeneous almost K\"ahler manifolds and the Chern-Einstein equation

Differential Geometry 2018-12-07 v2

Authors: Dmitri V. Alekseevsky , Fabio Podestà

Abstract

Given a non compact semisimple Lie group $G$ we describe all homogeneous spaces $G/L$ carrying an invariant almost K\"ahler 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.

Keywords

homogeneous almost kähler manifolds chern-einstein equation semisimple lie groups invariant almost kähler structure ricci form chern connection

Cite

@article{arxiv.1811.04068,
  title  = {Homogeneous almost K\"ahler manifolds and the Chern-Einstein equation},
  author = {Dmitri V. Alekseevsky and Fabio Podestà},
  journal= {arXiv preprint arXiv:1811.04068},
  year   = {2018}
}

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Homogeneous almost K\"ahler manifolds and the Chern-Einstein equation

Abstract

Keywords

Cite

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