Quarter-symmetric connection on an almost Hermitian manifold and on a Kähler manifold
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arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866916088817647616 |
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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 |