Anti-Kaehlerian Manifolds
数学物理
2007-05-23 v1 广义相对论与量子宇宙学
math.MP
摘要
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.
引用
@article{arxiv.math-ph/9906012,
title = {Anti-Kaehlerian Manifolds},
author = {A. Borowiec and M. Francaviglia and I. Volovich},
journal= {arXiv preprint arXiv:math-ph/9906012},
year = {2007}
}
备注
12 pages in LaTeX