English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

It is well known that the curvature tensor of a pseudo-Riemannian manifoldcan be decomposed with respect to the pseudo-orthogonal group into the sum ofthe Weyl conformal curvature tensor, the traceless part of the Ricci tensor andof the scalar curvature. A similar decomposition with respect to thepseudo-unitary group exists on a pseudo-K\"ahlerian manifold; instead of theWeyl tensor one obtains the Bochner tensor. In the present paper, the knowndecomposition with respect to the pseudo-orthogonal group of the covariantderivative of the curvature tensor of a pseudo-Riemannian manifold is refined.A decomposition with respect to the pseudo-unitary group of the covariantderivative of the curvature tensor for pseudo-K\"ahlerian manifolds isobtained. This defines natural classes of spaces generalizing locally symmetricspaces and Einstein spaces. It is shown that the values of the covariantderivative of the curvature tensor for a non-locally symmetricpseudo-Riemannian manifold with an irreducible connected holonomy groupdifferent from the pseudo-orthogonal and pseudo-unitary groups belong to anirreducible module of the holonomy group.

Covariant derivative of the curvature tensor of pseudo-K\"ahlerian manifolds