Three dimensional contact metric manifolds with vanishing . . .

We study 3-dimensional contact metric manifolds, the Jacobi operator, of which, vanishes identically. The local description and construction as well as some global results of this class of manifolds are given. Our results are followed by several examples

The curvature tensor of (\ka,\mu,\nu)-contact metric manifolds

We study the Riemann curvature tensor of (\kappa,\mu,\nu)-contact metric manifolds, which we prove to be completely determined in dimension 3, and we observe how it is affected by D_a-homothetic deformations. This prompts the definition and study of generalized (\kappa,\mu,\nu)-space forms and of the necessary and sufficient conditions for them to be conformally flat

Generalized (\kappa,\mu)-space forms

Generalized (\kappa ,\mu)-space forms are introduced and studied. We examine in depth the contact metric case and present examples for all possible dimensions. We also analyse the trans-Sasakian case.Comment: 20 pages, several changes have been done in this versio

Ricci collineations on 3-dimensional paracontact metric manifolds

We classify three-dimensional paracontact metric manifold whose Ricci operator Q is invariant along Reeb vector field, that is, L(xi)Q = 0