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