Elementary relative tractor calculus for Legendrean contact structures

Michał Andrzej Wasilewicz

Address: Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Vienna, Austria

E-mail: michal.wasilewicz@univie.ac.at

Abstract: For a manifold $M$ endowed with a Legendrean (or Lagrangean) contact structure $E\oplus F \subset TM$, we give an elementary construction of an invariant partial connection on the quotient bundle $TM/F$. This permits us to develop a naïve 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.

AMSclassification: primary 53D12.

Keywords: parabolic geometries, relative BGG conctruction, relative tractor calculus, Legendrean contact structures, Lagrangean contact structures, invariant differential operators, partial connections.

DOI: 10.5817/AM2022-5-339