On the structure of nearly pseudo-Kähler manifolds

Details On the structure of nearly pseudo-Kähler manifolds On the structure of nearly pseudo-Kähler manifolds

2009-12-17

arxiv.org/abs/0912.3266v1

Mathematics

Differential Geometry

to appear in Monatshefte f"ur Mathematik

Scientific paper

Firstly we give a condition to split off the K"ahler factor from a nearly pseudo-K"ahler manifold and apply this to get a structure result in dimension 8. Secondly we extend the construction of nearly K"ahler manifolds from twistor spaces to negatively curved quaternionic K"ahler manifolds and para-quaternionic K"ahler manifolds. The class of nearly pseudo-K"ahler manifolds obtained from this construction is characterized by a holonomic condition. The combination of these results enables us to give a classification result in (real) dimension 10. Moreover, we show that a strict nearly pseudo-K"ahler six-manifold is Einstein.

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