On conformally flat contact metric manifolds (Q1879095)

In this paper, conformally flat contact metric manifolds of dimension \(2n+1\), \(n>1\), are investigated. It is proven that a manifold of this type is Sasakian of constant curvature 1 if \(R(\cdot,\xi)\xi=-k(\eta\otimes\xi-I)\), where \(R\) and \(\eta\) are the Riemannian curvature form and the contact form of this manifold respectively, \(\xi\) the vector field defined by \(\eta(\xi)=1\), and \(k\) a smooth function on this manifold.