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

Abstract

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

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