$\ast$-conformal Einstein solitons on N(k)-contact metric manifolds
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866917599252578304 |
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| author | Das, Jhantu Halder, Kalyan Roy, Soumendu Bhattacharyya, Arindam |
| author_facet | Das, Jhantu Halder, Kalyan Roy, Soumendu Bhattacharyya, Arindam |
| contents | The main goal of this paper is devoted to N(k)-contact metric manifolds admitting $\ast$-conformal Einstein soliton and also $\ast$-conformal gradient Einstein soliton. In this settings the nature of the manifold, and the potential vector field, potential function of solitons are characterized, and conditions for the $\ast$-conformal Einstein soliton to be expanding, steady, or shrinking are also given. Furthermore, the nature of the potential vector field is evolved when the metric g of N(k)-contact metric manifold satisfies $\ast$-conformal gradient Einstein soliton. Finally, an illustrative example of a N(k)-contact metric manifold is discussed to verify our findings. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2402_17380 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $\ast$-conformal Einstein solitons on N(k)-contact metric manifolds Das, Jhantu Halder, Kalyan Roy, Soumendu Bhattacharyya, Arindam Differential Geometry Primary 53D15, Secondary 53C44, 35Q51 The main goal of this paper is devoted to N(k)-contact metric manifolds admitting $\ast$-conformal Einstein soliton and also $\ast$-conformal gradient Einstein soliton. In this settings the nature of the manifold, and the potential vector field, potential function of solitons are characterized, and conditions for the $\ast$-conformal Einstein soliton to be expanding, steady, or shrinking are also given. Furthermore, the nature of the potential vector field is evolved when the metric g of N(k)-contact metric manifold satisfies $\ast$-conformal gradient Einstein soliton. Finally, an illustrative example of a N(k)-contact metric manifold is discussed to verify our findings. |
| title | $\ast$-conformal Einstein solitons on N(k)-contact metric manifolds |
| topic | Differential Geometry Primary 53D15, Secondary 53C44, 35Q51 |
| url | https://arxiv.org/abs/2402.17380 |