Geometry of weak metric f-manifolds: a survey

2025/01/06 by Vladimir Rovenski, Rovenski, Vladimir · 1 citation
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2501.04048

openalex publication_date 2025/01/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A weak f-structure on a smooth manifold, introduced by the author and R. Wolak (2022), generalizes K. Yano's (1961) f-structure. This generalization allows us to revisit classical theory and discover new applications related to Killing vector fields, totally geodesic foliations, Ricci-type solitons, and Einstein-type metrics. This article reviews the results on weak metric f-manifolds, where the complex structure on the contact distribution of a metric f-structure is replaced with a nonsingular skew-symmetric tensor, and explores its distinguished classes.

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• Characterizations of weak almost \mathcal S-manifolds with curvature properties

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