On Weyl structures reducible in the direction of the Lee form
Abstract
A Weyl structure on a Riemannian manifold ( M , g ) (M,g) is a torsion-free linear connection ∇ \nabla such that there is a 1 1 -form θ \theta (called the Lee form) satisfying ∇ g = 2 θ ⊗ g \nabla g = 2\, \theta \otimes g . We examine the case in which there exists a ∇ \nabla -parallel distribution of codimension 1 1 on which the Lee form vanishes identically. We prove that if ( M , g ) (M,g) is complete with θ \theta closed, then the Weyl structure must be flat or exact. We apply this to prove the conjecture in [Eur. J. Math. 9 (2023), p. 4], namely, every homogeneous Kenmotsu manifold is isometric to the real hyperbolic space.
Fields of Study & Subjects
Advanced Algebra and Geometry
Geometric and Algebraic Topology
Quantum chaos and dynamical systems
Publication details
- Journal / source
- Proceedings of the American Mathematical Society
- Volume
- 154
- Issue
- 10
- Pages
- 4425–4438
- Publication date
- 15 April 2026
- Language
- EN