On complex Cartan spaces.
Analytic vector fields in a Hermitian manifold have been studied by various authors [3, 4, 6 & 7]. Boothby [2] and Goldberg [1] extended some of these results to Hermitian manifold with torsion. In this paper we define and study p-pseudo-analytic vector fields, which when p = 1, reduce to analytic vector fields as given in [1] and [2]. A necessary and sufficient condition for a vector field to be covariant (contravariant) p-pseudo-analytic has been obtained and their relationship with p-pseudo-harmonic...
On any real semisimple Lie group we consider a one-parameter family of left-invariant naturally reductive metrics. Their geodesic flow in terms of Killing curves, the Levi Civita connection and the main curvature properties are explicitly computed. Furthermore we present a group theoretical revisitation of a classical realization of all simply connected 3-dimensional manifolds with a transitive group of isometries due to L. Bianchi and É. Cartan. As a consequence one obtains a characterization of...