Geodesic
Elementary relative tractor calculus for Legendrean contact structures
Archivum mathematicum, Tome 58 (2022) no. 5, pp. 339-347 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
DOI : 10.5817/AM2022-5-339
Classification : 53D12
Keywords: parabolic geometries; relative BGG conctruction; relative tractor calculus; Legendrean contact structures; Lagrangean contact structures; invariant differential operators; partial connections 
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Wasilewicz, Michał Andrzej. Elementary relative tractor calculus for Legendrean contact structures. Archivum mathematicum, Tome 58 (2022) no. 5, pp. 339-347. doi: 10.5817/AM2022-5-339

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