On the Geometry of the Riemannian Curvature Tensor of Nearly Trans-Sasakian Manifolds
This paper presents the results of fundamental research into the geometry of the Riemannian curvature tensor of nearly trans-Sasakian manifolds. The components of the Riemannian curvature tensor on the space of the associated G-structure are counted, and the components of the Ricci tensor are calcul...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-08-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/12/9/837 |
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| author | Aligadzhi R. Rustanov |
| author_facet | Aligadzhi R. Rustanov |
| author_sort | Aligadzhi R. Rustanov |
| collection | DOAJ |
| description | This paper presents the results of fundamental research into the geometry of the Riemannian curvature tensor of nearly trans-Sasakian manifolds. The components of the Riemannian curvature tensor on the space of the associated G-structure are counted, and the components of the Ricci tensor are calculated. Some identities are obtained that are satisfied by the Riemannian curvature tensors and the Ricci tensor. A number of properties are proved that characterize nearly trans-Sasakian manifolds with a closed contact form. The structure of nearly trans-Sasakian manifolds with a closed contact form is obtained. Several classes are singled out in terms of second-order differential-geometric invariants, and their local structure is obtained. The k-nullity distribution of a nearly trans-Sasakian manifold is studied. |
| first_indexed | 2024-03-10T23:02:33Z |
| format | Article |
| id | doaj.art-7bb38a03cd664fb7b8887f7783732e55 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-10T23:02:33Z |
| publishDate | 2023-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-7bb38a03cd664fb7b8887f7783732e552023-11-19T09:32:25ZengMDPI AGAxioms2075-16802023-08-0112983710.3390/axioms12090837On the Geometry of the Riemannian Curvature Tensor of Nearly Trans-Sasakian ManifoldsAligadzhi R. Rustanov0Department of Higher Mathematics, Institute of Digital Technologies and Modeling in Construction, Moscow State University of Civil Engineering, 129337 Moscow, RussiaThis paper presents the results of fundamental research into the geometry of the Riemannian curvature tensor of nearly trans-Sasakian manifolds. The components of the Riemannian curvature tensor on the space of the associated G-structure are counted, and the components of the Ricci tensor are calculated. Some identities are obtained that are satisfied by the Riemannian curvature tensors and the Ricci tensor. A number of properties are proved that characterize nearly trans-Sasakian manifolds with a closed contact form. The structure of nearly trans-Sasakian manifolds with a closed contact form is obtained. Several classes are singled out in terms of second-order differential-geometric invariants, and their local structure is obtained. The k-nullity distribution of a nearly trans-Sasakian manifold is studied.https://www.mdpi.com/2075-1680/12/9/837nearly trans-Sasakian manifoldRiemannian curvature tensork-nullity distributionclosely cosymplectic manifold |
| spellingShingle | Aligadzhi R. Rustanov On the Geometry of the Riemannian Curvature Tensor of Nearly Trans-Sasakian Manifolds Axioms nearly trans-Sasakian manifold Riemannian curvature tensor k-nullity distribution closely cosymplectic manifold |
| title | On the Geometry of the Riemannian Curvature Tensor of Nearly Trans-Sasakian Manifolds |
| title_full | On the Geometry of the Riemannian Curvature Tensor of Nearly Trans-Sasakian Manifolds |
| title_fullStr | On the Geometry of the Riemannian Curvature Tensor of Nearly Trans-Sasakian Manifolds |
| title_full_unstemmed | On the Geometry of the Riemannian Curvature Tensor of Nearly Trans-Sasakian Manifolds |
| title_short | On the Geometry of the Riemannian Curvature Tensor of Nearly Trans-Sasakian Manifolds |
| title_sort | on the geometry of the riemannian curvature tensor of nearly trans sasakian manifolds |
| topic | nearly trans-Sasakian manifold Riemannian curvature tensor k-nullity distribution closely cosymplectic manifold |
| url | https://www.mdpi.com/2075-1680/12/9/837 |
| work_keys_str_mv | AT aligadzhirrustanov onthegeometryoftheriemanniancurvaturetensorofnearlytranssasakianmanifolds |