Nearly pseudo-Kähler and nearly para-Kähler six-manifolds
Lars SchäferLeibniz Universität Hannover, Germany
Fabian Schulte-HengesbachUniversität Hamburg, Germany
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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.