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@article{1385087, author = {Galaev, Anton}, article_number = {3}, doi = {http://dx.doi.org/10.1007/s10455-016-9533-1}, keywords = {Pseudo-Riemannian manifold; Pseudo-Kahlerian manifold; Curvature tensor; Covariant derivative of the curvature tensor; Second Bianchi identity}, language = {eng}, issn = {0232-704X}, journal = {Annals of Global Analysis and Geometry}, title = {Covariant derivative of the curvature tensor of pseudo-Kahlerian manifolds}, url = {https://link.springer.com/article/10.1007/s10455-016-9533-1}, volume = {51}, year = {2017} }
TY - JOUR ID - 1385087 AU - Galaev, Anton PY - 2017 TI - Covariant derivative of the curvature tensor of pseudo-Kahlerian manifolds JF - Annals of Global Analysis and Geometry VL - 51 IS - 3 SP - 245-265 EP - 245-265 PB - Kluwer Academic Publishers SN - 0232704X KW - Pseudo-Riemannian manifold KW - Pseudo-Kahlerian manifold KW - Curvature tensor KW - Covariant derivative of the curvature tensor KW - Second Bianchi identity UR - https://link.springer.com/article/10.1007/s10455-016-9533-1 L2 - https://link.springer.com/article/10.1007/s10455-016-9533-1 N2 - It is well known that the curvature tensor of a pseudo-Riemannian manifold can be decomposed with respect to the pseudo-orthogonal group into the sum of the Weyl conformal curvature tensor, the traceless part of the Ricci tensor and of the scalar curvature. A similar decomposition with respect to the pseudo-unitary group exists on a pseudo-Kahlerian manifold; instead of the Weyl tensor one obtains the Bochner tensor. In the present paper, the known decomposition with respect to the pseudo-orthogonal group of the covariant derivative of the curvature tensor of a pseudo-Riemannian manifold is refined. A decomposition with respect to the pseudo-unitary group of the covariant derivative of the curvature tensor for pseudo-Kahlerian manifolds is obtained. This defines natural classes of spaces generalizing locally symmetric spaces and Einstein spaces. It is shown that the values of the covariant derivative of the curvature tensor for a non-locally symmetric pseudo-Riemannian manifold with an irreducible connected holonomy group different from the pseudo-orthogonal and pseudo-unitary groups belong to an irreducible module of the holonomy group. ER -
GALAEV, Anton. Covariant derivative of the curvature tensor of pseudo-Kahlerian manifolds. \textit{Annals of Global Analysis and Geometry}. Kluwer Academic Publishers, 2017, roč.~51, č.~3, s.~245-265. ISSN~0232-704X. Dostupné z: https://dx.doi.org/10.1007/s10455-016-9533-1.
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