Curvature tensors and hyperbolic solitons on Lorentzian trans-Sasakian space form
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866911169455849472 |
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| author | Mondal, Bidhan Basu, Nirabhra Bhattacharyya, Arindam |
| author_facet | Mondal, Bidhan Basu, Nirabhra Bhattacharyya, Arindam |
| contents | Lorantzian trans-Sasakian space form is a special type of space form in which the nature of even and odd dimensional space form both exist. Various curvature tensors with respect to Levi-Civita connection on the space form are derived in this paper. We have shown that if an odd-dimensional Lorentzian trans-Sasakian space form admits a hyperbolic Ricci soliton and hyperbolic conformal Ricci soliton then they will be $η$-Einstein. We also obtained the conditions for the solitons to be expanding, steady or shrinking. Finally, an example has been constructed which justifies the results obtained. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_18318 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Curvature tensors and hyperbolic solitons on Lorentzian trans-Sasakian space form Mondal, Bidhan Basu, Nirabhra Bhattacharyya, Arindam Differential Geometry Lorantzian trans-Sasakian space form is a special type of space form in which the nature of even and odd dimensional space form both exist. Various curvature tensors with respect to Levi-Civita connection on the space form are derived in this paper. We have shown that if an odd-dimensional Lorentzian trans-Sasakian space form admits a hyperbolic Ricci soliton and hyperbolic conformal Ricci soliton then they will be $η$-Einstein. We also obtained the conditions for the solitons to be expanding, steady or shrinking. Finally, an example has been constructed which justifies the results obtained. |
| title | Curvature tensors and hyperbolic solitons on Lorentzian trans-Sasakian space form |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2509.18318 |