# Anti-Kaehlerian Manifolds

@article{Borowiec1999AntiKaehlerianM, title={Anti-Kaehlerian Manifolds}, author={Andrzej Borowiec and Mauro Francaviglia and Igor V. Volovich}, journal={arXiv: Mathematical Physics}, year={1999} }

An anti-Kaehlerian manifold is a complex manifold with an anti-Hermitian metric and a parallel almost complex structure. It is shown that a metric on such a manifold must be the real part of a holomorphic metric. It is proved that all odd Chern numbers of an anti-Kaehlerian manifold vanish and that complex parallelisable manifolds (in particular the factor space G/D of a complex Lie group G over the discrete subgroup D) are anti-Kaehlerian manifolds. A method of generating new solutions of…

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