Conformally flat contact metric manifolds with \(Q\xi=\varrho\xi\) (Q1875904)

The authors study conformally flat contact metric manifolds whose characteristic vector field is an eigenfield of the Ricci tensor. The main result of the paper is the following classification theorem: Let a Riemannian manifold \((M^{2n+1}, g)\), \(n> 1\), be a conformally flat contact metric manifold whose characteristic vector field is an eigenvector of the Ricci operator \(Q\) at every point. Then \((M^{2n+1}, g)\) is of constant sectional curvature.