2010arXiv (Cornell University)Open access

Decomposition of the covariant derivative of the curvature tensor of a pseudo-K\"ahlerian manifold

Anton S. Galaev

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Abstract

The decompositions of the curvature tensors of pseudo-Riemannian and pseudo-K\ahlerian manifolds are reviewed. The known decomposition of the covariant derivative of the curvature tensor of a pseudo-Riemannian manifold is refined. A decomposition of the covariant derivative of the curvature tensor of a pseudo-K\ahlerian manifolds is obtained.

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The decompositions of the curvature tensors of pseudo-Riemannian and pseudo-K\ahlerian manifolds are reviewed. The known decomposition of the covariant derivative of the curvature tensor of a pseudo-Riemannian manifold is refined. A decomposition of the covariant derivative of the curvature tensor of a pseudo-K\ahlerian manifolds is obtained.

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Available abstract

The decompositions of the curvature tensors of pseudo-Riemannian and pseudo-K\ahlerian manifolds are reviewed. The known decomposition of the covariant derivative of the curvature tensor of a pseudo-Riemannian manifold is refined. A decomposition of the covariant derivative of the curvature tensor of a pseudo-K\ahlerian manifolds is obtained.

Key concepts: Covariant derivative, Riemann curvature tensor, Curvature of Riemannian manifolds, Ricci decomposition, Ricci curvature, Curvature, Covariant transformation, Manifold (fluid mechanics)

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