Vertical tangential invariants on some foliated lagrange spaces

Abstract

In this paper we consider a decomposition of tangentially differential forms with respect to the lifted foliation FT to the tangent bundle of a Lagrange space M,L endowed with a regular foliation manifold (TM, F T. First, starting from a natural decomposition of the tangential exterior derivative along the leaves of FT, we define some vertical tangential cohomology groups of the foliated manifold TM, FT, we prove a Poincaré lemma for the vertical tangential derivative and we obtain a de Rham theorem for this cohomology. Next, in a classical way, we construct vertical tangential characteristic classes of tangentially smooth complex bundles over the foliated manifold TM, FT. © 2013 World Scientific Publishing Company.