$η$-Ricci solitons and $η$-Einstein metrics on weak $β$-Kenmotsu $f$-manifolds
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915306790715392 |
|---|---|
| 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, which generalize the flow of the Reeb vector field on contact manifolds to higher dimensions. Weak metric structures introduced by V. Rovenski and R. Wolak as a generalization of Hermitian and Kähler structures, as well as $f$-structures, allow a fresh look at the classical theory. In this paper, we study a new $f$-structure of this kind, called the weak $β$-Kenmotsu $f$-structure, as a generalization of K. Kenmotsu's concept. We prove that a weak $β$-Kenmotsu $f$-manifold is locally a twisted product of the Euclidean space and a weak Kähler manifold. Our main results show that such manifolds with $β=const$ and equipped with an $η$-Ricci soliton structure whose potential vector field satisfies certain conditions are $η$-Einstein manifolds of constant scalar curvature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_14125 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $η$-Ricci solitons and $η$-Einstein metrics on weak $β$-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, which generalize the flow of the Reeb vector field on contact manifolds to higher dimensions. Weak metric structures introduced by V. Rovenski and R. Wolak as a generalization of Hermitian and Kähler structures, as well as $f$-structures, allow a fresh look at the classical theory. In this paper, we study a new $f$-structure of this kind, called the weak $β$-Kenmotsu $f$-structure, as a generalization of K. Kenmotsu's concept. We prove that a weak $β$-Kenmotsu $f$-manifold is locally a twisted product of the Euclidean space and a weak Kähler manifold. Our main results show that such manifolds with $β=const$ and equipped with an $η$-Ricci soliton structure whose potential vector field satisfies certain conditions are $η$-Einstein manifolds of constant scalar curvature. |
| title | $η$-Ricci solitons and $η$-Einstein metrics on weak $β$-Kenmotsu $f$-manifolds |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2412.14125 |