Nearly pseudo-Kähler and nearly para-Kähler six-manifolds

Details Nearly pseudo-Kähler and nearly para-Kähler six-manifolds Nearly pseudo-Kähler and nearly para-Kähler six-manifolds

2009-12-16

arxiv.org/abs/0912.3271v1

Mathematics

Differential Geometry

to appear in Handbook of pseudo-Riemannian Geometry and Supersymmetry, edited by V. Cortes

Scientific paper

The subject of this paper is six-dimensional nearly (para-)K\"ahler geometry with pseudo-Riemannian metrics. Firstly, we derive the analogue of the well-known exterior differential system characterising a nearly K\"ahler manifold and prove applications to the automorphism group of a nearly (para-)K\"ahler structure. Secondly, we prove existence and uniqueness results for left-invariant nearly (para-)K\"ahler structures on Lie groups $G \times G$ where $G$ is three-dimensional and simple.

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