Weak quasi contact metric manifolds and new characteristics of K-contact and Sasakian manifolds
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914972633661440 |
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| author | Rovenski, Vladimir |
| author_facet | Rovenski, Vladimir |
| contents | Quasi contact metric manifolds (introduced by Y. Tashiro and then studied by several authors) are a natural extension of the contact metric manifolds. Weak almost contact metric manifolds, i.e., the linear complex structure on the contact distribution is replaced by a nonsingular skew-symmetric tensor, were defined by the author and R. Wolak. In this paper, we study a weak analogue of quasi contact metric manifolds. Our main results generalize some well known theorems and provide new criterions for K-contact and Sasakian manifolds in terms of conditions on the curvature tensor and other geometric objects associated with the weak quasi-contact metric structure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_02752 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Weak quasi contact metric manifolds and new characteristics of K-contact and Sasakian manifolds Rovenski, Vladimir Differential Geometry Quasi contact metric manifolds (introduced by Y. Tashiro and then studied by several authors) are a natural extension of the contact metric manifolds. Weak almost contact metric manifolds, i.e., the linear complex structure on the contact distribution is replaced by a nonsingular skew-symmetric tensor, were defined by the author and R. Wolak. In this paper, we study a weak analogue of quasi contact metric manifolds. Our main results generalize some well known theorems and provide new criterions for K-contact and Sasakian manifolds in terms of conditions on the curvature tensor and other geometric objects associated with the weak quasi-contact metric structure. |
| title | Weak quasi contact metric manifolds and new characteristics of K-contact and Sasakian manifolds |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2410.02752 |