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Title: Elementary relative tractor calculus for Legendrean contact structures (English)
Author: Wasilewicz, Michał Andrzej
Language: English
Journal: Archivum Mathematicum
ISSN: 0044-8753 (print)
ISSN: 1212-5059 (online)
Volume: 58
Issue: 5
Year: 2022
Pages: 339-347
Summary lang: English
Category: math
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. (English)
Keyword: parabolic geometries
Keyword: relative BGG conctruction
Keyword: relative tractor calculus
Keyword: Legendrean contact structures
Keyword: Lagrangean contact structures
Keyword: invariant differential operators
Keyword: partial connections
MSC: 53D12
idZBL: Zbl 07655752
idMR: MR4529823
DOI: 10.5817/AM2022-5-339
Date available: 2022-11-28T12:34:45Z
Last updated: 2023-03-13
Stable URL:
Reference: [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, MR 2532439, 10.1090/surv/154/03
Reference: [2] Čap, A., Souček, V.: Relative BGG sequences: I. Algebra.J. Algebra 463 (2016), 188–210. MR 3527545, 10.1016/j.jalgebra.2016.06.007
Reference: [3] Čap, A., Souček, V.: Relative BGG sequences; II. BGG machinery and invariant operators.Adv. Math. 320 (2017), 1009–1062. MR 3709128, 10.1016/j.aim.2017.09.016
Reference: [4] Takeuchi, M.: Legendrean contact structures on projective cotangent bundles.Osaka J. Math. 31 (4) (1994), 837–860. MR 1315010


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