Anti-Kählerian manifolds

✍ Scribed by Andrzej Borowiec; Mauro Francaviglia; Igor Volovich

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 65 KB
• Volume: 12
• Category: Article
• ISSN: 0926-2245
• DOI: 10.1016/s0926-2245(00)00017-6

✦ Synopsis

An anti-Kählerian 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-Kählerian 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-Kählerian manifolds. A method of generating new solutions of Einstein equations by using the theory of anti-Kählerian manifolds is presented.