1999/06/13 by A. Borowiec, M. Francaviglia, I. Volovich
Physics and Astronomy · Mathematics · #math-ph #gr-qc #math.MP
published as Differ.Geom.Appl. 12 (2000) 281 · 12 pages in LaTeX
arxiv created 1999/06/13 · arxiv updated 2009/11/30
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.