Quarter-symmetric connection on an almost Hermitian manifold and on a Kähler manifold

Fuente: arXiv
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Main Authors: Zlatanović, Milan, Maksimović, Miroslav
Format: Preprint
Published: 2022
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author Zlatanović, Milan
Maksimović, Miroslav
author_facet Zlatanović, Milan
Maksimović, Miroslav
contents The paper observes an almost Hermitian manifold as an example of a generalized Riemannian manifold and examines the application of a quarter-symmetric connection on the almost Hermitian manifold. The almost Hermitian manifold with quarter-symmetric connection preserving the generalized Riemannian metric is actually the Kähler manifold. Observing the six linearly independent curvature tensors with respect to the quarter-symmetric connection, we construct tensors that do not depend on the quarter-symmetric connection generator. One of them coincides with the Weyl projective curvature tensor of symmetric metric $g$. Also, we obtain the relations between the Weyl projective curvature tensor and the holomorphically projective curvature tensor. Moreover, we examine the properties of curvature tensors when some tensors are hybrid.
format Preprint
id arxiv_https___arxiv_org_abs_2212_01123
institution arXiv
publishDate 2022
record_format arxiv
spellingShingle Quarter-symmetric connection on an almost Hermitian manifold and on a Kähler manifold
Zlatanović, Milan
Maksimović, Miroslav
Differential Geometry
53B05, 53B35, 53C05, 53C15
The paper observes an almost Hermitian manifold as an example of a generalized Riemannian manifold and examines the application of a quarter-symmetric connection on the almost Hermitian manifold. The almost Hermitian manifold with quarter-symmetric connection preserving the generalized Riemannian metric is actually the Kähler manifold. Observing the six linearly independent curvature tensors with respect to the quarter-symmetric connection, we construct tensors that do not depend on the quarter-symmetric connection generator. One of them coincides with the Weyl projective curvature tensor of symmetric metric $g$. Also, we obtain the relations between the Weyl projective curvature tensor and the holomorphically projective curvature tensor. Moreover, we examine the properties of curvature tensors when some tensors are hybrid.
title Quarter-symmetric connection on an almost Hermitian manifold and on a Kähler manifold
topic Differential Geometry
53B05, 53B35, 53C05, 53C15
url https://arxiv.org/abs/2212.01123