GEOMETRY OF t-PROJECTIVE STRUCTURES

The main purpose of this paper is to define and study t-projective structure on even dimensional manifold M as a certain reduction of the second order frame bundle over M.This t-structure reveals some similarities to the projective structures of Kobayashi-Nagano [KN1] but it is a completely different one.The structure group is the isotropy group of the tangent bundle of the projective space.With the t-structure we associate in a natural way the so called normal Cartan connection and we investigate its properties.We show that t-structures are closely related the almost tangent structures on M. Finally, we consider the natural cross sections and we derive the coefficients of the normal connection of a t-projective structure.