Geometry of weak metric $f$-manifolds: a survey

Vladimir Rovenski

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arXiv · 2501.04048

Geometry of weak metric $f$-manifolds: a survey

Vladimir Rovenski

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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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BibTeX RIS

Vladimir Rovenski. 2025-01-06. Geometry of weak metric $f$-manifolds: a survey. https://arxiv.org/abs/2501.04048

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