(κ, μ, υ = const.)-contact metric manifolds with ξ(IM)=0

Abstract

We give a local classification of (kappa, mu, upsilon = const.)-contact metric manifold (M, phi, xi, eta, g) with kappa < 1 which satisfies the condition" the Boeckx invariant function I-M = 1-mu/2/root 1-kappa is constant along the integral curves of the characteristic vector field xi".