  In this study, we deal with the local structure of curves and surfaces
immersed in a pseudo-isotropic space I_{p}^{3} that is a particular
Cayley-Klein space. We provide the formulas of curvature, torsion and Frenet
trihedron in order for spacelike and timelike curves. The causal character of
all admissible surfaces in I_{p}^{3} has to be timelike or lightlike up to its
absolute. We introduce the formulas of Gaussian and mean curvature for timelike
surfaces in I_{p}^{3}. As applications, we describe the surfaces of revolution
which are the orbits of a plane curve under a hyperbolic rotation with constant
Gaussian and mean curvature.
