Geometry of Harmonic Nearly Trans-Sasakian Manifolds
This paper considers a class of nearly trans-Sasakian manifolds. The local structure of nearly trans-Sasakian structures with a closed contact form and a closed Lee form is obtained. It is proved that the class of nearly trans-Sasakian manifolds with a closed contact form and a closed Lee form coinc...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-07-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/12/8/744 |
| _version_ | 1797585524881358848 |
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| author | Aligadzhi R. Rustanov |
| author_facet | Aligadzhi R. Rustanov |
| author_sort | Aligadzhi R. Rustanov |
| collection | DOAJ |
| description | This paper considers a class of nearly trans-Sasakian manifolds. The local structure of nearly trans-Sasakian structures with a closed contact form and a closed Lee form is obtained. It is proved that the class of nearly trans-Sasakian manifolds with a closed contact form and a closed Lee form coincides with the class of almost contact metric manifolds with a closed contact form locally conformal to the closely cosymplectic manifolds. A wide class of harmonic nearly trans-Sasakian manifolds has been identified (i.e., nearly trans-Sasakian manifolds with a harmonic contact form) and an exhaustive description of the manifolds of this class is obtained. Also, examples of harmonic nearly trans-Sasakian manifolds are given. |
| first_indexed | 2024-03-11T00:07:22Z |
| format | Article |
| id | doaj.art-5117930b8a874ff49153899e0e2e9adf |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-11T00:07:22Z |
| publishDate | 2023-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-5117930b8a874ff49153899e0e2e9adf2023-11-19T00:14:35ZengMDPI AGAxioms2075-16802023-07-0112874410.3390/axioms12080744Geometry of Harmonic Nearly Trans-Sasakian ManifoldsAligadzhi R. Rustanov0Department of Higher Mathematics, Institute of Digital Technologies and Modeling in Construction, Moscow State University of Civil Engineering, Moscow 129337, RussiaThis paper considers a class of nearly trans-Sasakian manifolds. The local structure of nearly trans-Sasakian structures with a closed contact form and a closed Lee form is obtained. It is proved that the class of nearly trans-Sasakian manifolds with a closed contact form and a closed Lee form coincides with the class of almost contact metric manifolds with a closed contact form locally conformal to the closely cosymplectic manifolds. A wide class of harmonic nearly trans-Sasakian manifolds has been identified (i.e., nearly trans-Sasakian manifolds with a harmonic contact form) and an exhaustive description of the manifolds of this class is obtained. Also, examples of harmonic nearly trans-Sasakian manifolds are given.https://www.mdpi.com/2075-1680/12/8/744nearly trans-Sasakian structurelinear expansionalmost Hermitian structureharmonic nearly trans-Sasakian structureKenmotsu structure |
| spellingShingle | Aligadzhi R. Rustanov Geometry of Harmonic Nearly Trans-Sasakian Manifolds Axioms nearly trans-Sasakian structure linear expansion almost Hermitian structure harmonic nearly trans-Sasakian structure Kenmotsu structure |
| title | Geometry of Harmonic Nearly Trans-Sasakian Manifolds |
| title_full | Geometry of Harmonic Nearly Trans-Sasakian Manifolds |
| title_fullStr | Geometry of Harmonic Nearly Trans-Sasakian Manifolds |
| title_full_unstemmed | Geometry of Harmonic Nearly Trans-Sasakian Manifolds |
| title_short | Geometry of Harmonic Nearly Trans-Sasakian Manifolds |
| title_sort | geometry of harmonic nearly trans sasakian manifolds |
| topic | nearly trans-Sasakian structure linear expansion almost Hermitian structure harmonic nearly trans-Sasakian structure Kenmotsu structure |
| url | https://www.mdpi.com/2075-1680/12/8/744 |
| work_keys_str_mv | AT aligadzhirrustanov geometryofharmonicnearlytranssasakianmanifolds |