Handbook of Pseudo-Riemannian Geometry and Supersymmetry

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pp: 425–453

DOI: 10.4171/079-1/12

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

Lars Schäfer[1] and Fabian Schulte-Hengesbach

(1) Leibniz Universität Hannover, Germany

The subject of this chapter 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 × G where G is three-dimensional and simple.

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