2025/07/23 by Jiménez, José Luis Carmona
#53A30 #53C05 #53C15 #53C30 #53D15 #Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.2507.17496
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.