Elementary relative tractor calculus for Legendrean contact structures

Abstract

. For a manifold M endowed with a Legendrean (or Lagrangean) contact structure E ⊕ F ⊂ TM , we give an elementary construction of an invariant partial connection on the quotient bundle TM/F . This permits us to develop a na¨ıve version of relative tractor calculus and to construct a second order invariant differential operator, which turns out to be the first relative BGG operator induced by the partial connection.