$\ast$-$η$-Ricci solitons on weak Kenmotsu $f$-manifolds
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908637145858048 |
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| author | Rovenski, Vladimir |
| author_facet | Rovenski, Vladimir |
| contents | Recent interest among geometers in $f$-structures of K. Yano is due to the study of topology and dynamics of contact foliations and generalized A. Weinstein conjectures. Weak metric $f$-structures, introduced by the author and R. Wolak as a generalization of Hermitian structure, as well as $f$-structure allow for a fresh perspective on the classical theory. An important case of such manifolds, which is locally a twisted product, is a weak $βf$-Kenmotsu manifold defined as a generalization of K. Kenmotsu's concept. In this paper, the concept of the $\ast$-Ricci tensor of S. Tashibana is adapted to weak metric $f$-manifolds, the interaction of $\ast$-$η$-Ricci soliton with the weak $βf$-Kenmotsu structure is studied and new characteristics of $η$-Einstein metrics are obtained. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_08973 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $\ast$-$η$-Ricci solitons on weak Kenmotsu $f$-manifolds Rovenski, Vladimir Differential Geometry Recent interest among geometers in $f$-structures of K. Yano is due to the study of topology and dynamics of contact foliations and generalized A. Weinstein conjectures. Weak metric $f$-structures, introduced by the author and R. Wolak as a generalization of Hermitian structure, as well as $f$-structure allow for a fresh perspective on the classical theory. An important case of such manifolds, which is locally a twisted product, is a weak $βf$-Kenmotsu manifold defined as a generalization of K. Kenmotsu's concept. In this paper, the concept of the $\ast$-Ricci tensor of S. Tashibana is adapted to weak metric $f$-manifolds, the interaction of $\ast$-$η$-Ricci soliton with the weak $βf$-Kenmotsu structure is studied and new characteristics of $η$-Einstein metrics are obtained. |
| title | $\ast$-$η$-Ricci solitons on weak Kenmotsu $f$-manifolds |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2506.08973 |