Geometry of Weak Metric f -Manifolds: A Survey

Vladimir Rovenski ()
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Vladimir Rovenski: Department of Mathematics, University of Haifa, Haifa 3498838, Israel

Mathematics, 2025, vol. 13, issue 4, 1-24

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 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.

Keywords: metric f -structure; Killing vector field; totally geodesic foliation; ? -Einstein metric; almost S -structure; almost C -structure; ? -Ricci soliton; f -K-manifold; ? -Kenmotsu; f -manifold (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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