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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.

MSC:

53D12 Lagrangian submanifolds; Maslov index
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[1] Čap, A.; Slovák, J., Parabolic geometries. I, Mathematical Surveys and Monographs, vol. 154, AMS, Providence, RI, 2009, Background and general theory · Zbl 1183.53002 · doi:10.1090/surv/154/03
[2] Čap, A.; Souček, V., Relative BGG sequences: I. Algebra, J. Algebra 463 (2016), 188-210 · Zbl 1380.17009 · doi:10.1016/j.jalgebra.2016.06.007
[3] Čap, A.; Souček, V., Relative BGG sequences; II. BGG machinery and invariant operators, Adv. Math. 320 (2017), 1009-1062 · Zbl 1418.17022 · doi:10.1016/j.aim.2017.09.016
[4] Takeuchi, M., Legendrean contact structures on projective cotangent bundles, Osaka J. Math. 31 (4) (1994), 837-860 · Zbl 0830.53028
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