Geometry of weak metric $f$-manifolds: a survey
Differential Geometry
2025-01-17 v2
Abstract
A weak -structure on a smooth manifold, introduced by the author and R. Wolak (2022), generalizes K. Yano's (1961) -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 -manifolds, where the complex structure on the contact distribution of a metric -structure is replaced with a nonsingular skew-symmetric tensor, and explores its distinguished classes.
Keywords
Cite
@article{arxiv.2501.04048,
title = {Geometry of weak metric $f$-manifolds: a survey},
author = {Vladimir Rovenski},
journal= {arXiv preprint arXiv:2501.04048},
year = {2025}
}
Comments
22 pages. arXiv admin note: text overlap with arXiv:2306.07102, arXiv:2412.14125