On the structure of nearly pseudo-K\"ahler manifolds
Differential Geometry
2009-12-18 v1
Abstract
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.
Keywords
Cite
@article{arxiv.0912.3266,
title = {On the structure of nearly pseudo-K\"ahler manifolds},
author = {Lars Schäfer},
journal= {arXiv preprint arXiv:0912.3266},
year = {2009}
}
Comments
to appear in Monatshefte f"ur Mathematik