Einstein-Weyl structure and contact geometry (Q2073679)

In the paper under review, the author studies Einstein-Weyl structure on \(K\)-contact and contact metric manifolds satisfying certain condition on the Weyl curvature tensor. Firstly it is proven that these structures are Einstein and Sasakian. Secondly, it is shown that a \((k, \mu)\)-contact manifold admitting a closed Einstein-Weyl structure is either locally isometric up to a \(D\)-homothetic transformation to the unit tangent bundle of certain space of constant curvature different from \(1\), or is compact Einstein and Sasakian.