ON THE CLASSIFICATION OF CONTACT RIEMANNIAN MANIFOLDS SATISFYING THE CONDITION (C)

Given a contact form (eta), there is a one-to-one correspondence between the Riemannian structures (eta,g) and the CR-structures (eta,L). It is interesting to study the interaction between the two associated structures. We approach the geometry of contact Riemannian manifolds in connection with their associated CR-structures. In this context, for a contact Riemannian manifold (M;eta,g) we consider the Jacobi-type operator R(\dot\gamma)=R(.,(dot\gamma))dot\gamma along a self-parallel curve (gamma) with respect to the (generalized) Tanaka connection (hatbnabla).