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Keywords = f-Kenmotsu manifolds

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15 pages, 325 KB  
Article
η-Ricci Solitons on Weak β-Kenmotsu f-Manifolds
by Vladimir Rovenski
Mathematics 2025, 13(11), 1734; https://doi.org/10.3390/math13111734 - 24 May 2025
Cited by 1 | Viewed by 448
Abstract
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 the [...] Read more.
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 the author and R. Wolak as a generalization of Hermitian and Kähler structures, as well as f-structures, allow for a fresh perspective on 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 a locally 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. Full article
(This article belongs to the Special Issue Differential Geometric Structures and Their Applications)
24 pages, 395 KB  
Review
Geometry of Weak Metric f-Manifolds: A Survey
by Vladimir Rovenski
Mathematics 2025, 13(4), 556; https://doi.org/10.3390/math13040556 - 8 Feb 2025
Cited by 2 | Viewed by 999
Abstract
The interest of geometers in f-structures is motivated by the study of the dynamics of contact foliations, as well as their applications in physics. A weak f-structure on a smooth manifold, introduced by the author and R. Wolak, generalizes K. Yano’s [...] Read more.
The interest of geometers in f-structures is motivated by the study of the dynamics of contact foliations, as well as their applications in physics. A weak f-structure on a smooth manifold, introduced by the author and R. Wolak, generalizes K. Yano’s f-structure. This generalization allows us to revisit classical theory and discover applications of Killing vector fields, totally geodesic foliations, Ricci-type solitons, and Einstein-type metrics. This article reviews the results regarding weak metric f-manifolds and their distinguished classes. Full article
(This article belongs to the Special Issue Recent Studies in Differential Geometry and Its Applications)
15 pages, 289 KB  
Article
Biharmonic Maps on f-Kenmotsu Manifolds with the Schouten–van Kampen Connection
by Hichem El hendi
Mathematics 2023, 11(8), 1905; https://doi.org/10.3390/math11081905 - 17 Apr 2023
Cited by 2 | Viewed by 1471
Abstract
The object of the present paper was to study biharmonic maps on f-Kenmotsu manifolds and f-Kenmotsu manifolds with the Schouten–van Kampen connection. With the help of this connection, our results provided important insights related to harmonic and biharmonic maps. Full article
(This article belongs to the Special Issue Geometry of Manifolds and Applications)
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