Existence, Stability, and Geometric Implications of $\ast$-$η$-Schouten Solitons on Kenmotsu Manifolds
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866916044799475712 |
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| author | Pallei, Tejswani Roy, Soumendu |
| author_facet | Pallei, Tejswani Roy, Soumendu |
| contents | In this manuscript, we investigate the characterizations of $\ast$-$η$-Schouten solitons on a Kenmotsu manifold when the potential vector field is torse-forming. We determine the nature of the soliton and derive the scalar curvature for a Kenmotsu manifold admitting a $\ast$-$η$-Schouten soliton. Further, we establish several conditions associated with the $\ast$-$η$-Schouten soliton. We also study the characterization of the vector field under the assumption that the manifold satisfies the $\ast$-$η$-Schouten soliton equation. Moreover, certain applications of torse-forming vector fields are discussed in the setting of $\ast$-$η$-Schouten solitons on Kenmotsu manifolds. In addition, we examine infinitesimal CL-transformations and the Schouten-Van Kampen connection on Kenmotsu manifolds whose metrics admit $\ast$-$η$-Schouten solitons. Finally, an example of a 3-dimensional Kenmotsu manifold admitting a $\ast$-$η$-Schouten soliton is constructed to verify the obtained results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_25825 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Existence, Stability, and Geometric Implications of $\ast$-$η$-Schouten Solitons on Kenmotsu Manifolds Pallei, Tejswani Roy, Soumendu Differential Geometry In this manuscript, we investigate the characterizations of $\ast$-$η$-Schouten solitons on a Kenmotsu manifold when the potential vector field is torse-forming. We determine the nature of the soliton and derive the scalar curvature for a Kenmotsu manifold admitting a $\ast$-$η$-Schouten soliton. Further, we establish several conditions associated with the $\ast$-$η$-Schouten soliton. We also study the characterization of the vector field under the assumption that the manifold satisfies the $\ast$-$η$-Schouten soliton equation. Moreover, certain applications of torse-forming vector fields are discussed in the setting of $\ast$-$η$-Schouten solitons on Kenmotsu manifolds. In addition, we examine infinitesimal CL-transformations and the Schouten-Van Kampen connection on Kenmotsu manifolds whose metrics admit $\ast$-$η$-Schouten solitons. Finally, an example of a 3-dimensional Kenmotsu manifold admitting a $\ast$-$η$-Schouten soliton is constructed to verify the obtained results. |
| title | Existence, Stability, and Geometric Implications of $\ast$-$η$-Schouten Solitons on Kenmotsu Manifolds |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2605.25825 |