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Geometry of t-projective structures

Miernowski A., Mozgawa W.

Demonstratio Mathematica

2002

Vol. 35, nr 2

391-403

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.