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This is a Quantitative Study study.

October 8, 2025Open Access

On Weyl structures reducible in the direction of the Lee form

Key Points

The study finds that Weyl structures in complete manifolds must be flat or exact when the Lee form is closed.
This research demonstrates that a parallel distribution with zero Lee form leads to significant geometric constraints.
The application of results shows that homogeneous Kenmotsu manifolds are isometric to hyperbolic spaces.
Results suggest broader implications for understanding Riemannian geometries and connections in manifolds.

Abstract

A Weyl structure on a Riemannian manifold (M, g) is a torsion-free linear connection such that there is a 1-form θ (called the Lee form) satisfying g = 2\, θ g. We examine the case in which there exists a -parallel distribution of codimension 1 on which the Lee form vanishes identically. We prove that if (M, g) is complete with θ closed, then the Weyl structure must be flat or exact. We apply this to show that every homogeneous Kenmotsu manifold is isometric to the real hyperbolic space.

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Cite This Study

José Luis Carmona Jiménez (Wed,) studied this question.

synapsesocial.com/papers/68e6860af44b9035634c20b0 https://doi.org/https://doi.org/10.48550/arxiv.2507.17496

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