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Anti-Kaehlerian Manifolds

A. Borowiec·M. Francaviglia·I. Volovich
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Abstract

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 Einstein equations by using the theory of anti-Kaehlerian manifolds is presented.

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A. Borowiec, M. Francaviglia, I. Volovich. 1999-06-13. Anti-Kaehlerian Manifolds. https://arxiv.org/abs/math-ph/9906012

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