Elementary relative tractor calculus for Legendrean contact structures. (English) Zbl 07655752

Summary: 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.


53D12 Lagrangian submanifolds; Maslov index
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