• Corpus ID: 117986772

Anti-Kaehlerian Manifolds

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



Almost-complex and almost-product Einstein manifolds from a variational principle

It is shown that the first-order (Palatini) variational principle for a generic nonlinear metric-affine Lagrangian depending on the (symmetrized) Ricci square invariant leads to an almost-product

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Hermitian and Kahlerian geometry in relativity

Complex structures on vector spaces.- Complex manifolds.- Vectors and tensors on a complex manifold.- Almost complex manifolds.- Hermitian and Kahlerian manifolds.- Review of general relativity.-

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