We study conformally flat Lorentzian three-manifolds which are either semi-symmetric or pseudo-symmetric. Their complete classification is obtained under hypotheses of local homogeneity and curvature homogeneity. Moreover, examples which are not curvature homogeneous are described.
We expound some results about the relationships between the Jacobi operators with respect to null vectors on a Lorentzian S-manifold and the Jacobi operators with respect to particular spacelike unit vectors. We study the number of the eigenvalues of such operators on Lorentzian S-manifolds satisfying the φ-null Osserman condition, under suitable assumptions on the dimension of the manifold. Then, we provide in full generality a new curvature characterization for Lorentzian S-manifolds and we use...
The notion of ``hyperbolic'' angle between any two time-like directions in the Lorentzian plane was properly defined and studied by Birman and Nomizu [1,2]. In this article, we define the notion of hyperbolic angle between any two non-null directions in and we define a measure on the set of these hyperbolic angles. As an application, we extend Scofield's work on the Euclidean curves of constant precession [9] to the Lorentzian setting, thus expliciting space-like curves in whose natural equations...