Elementary relative tractor calculus for Legendrean contact structures

Michał Andrzej Wasilewicz

Archivum Mathematicum (2022)

  • Volume: 058, Issue: 5, page 339-347
  • ISSN: 0044-8753

Abstract

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For a manifold M endowed with a Legendrean (or Lagrangean) contact structure E ⊕ F ⊂ T M , we give an elementary construction of an invariant partial connection on the quotient bundle T M / 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.

How to cite

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Wasilewicz, Michał Andrzej. "Elementary relative tractor calculus for Legendrean contact structures." Archivum Mathematicum 058.5 (2022): 339-347. <http://eudml.org/doc/298904>.

@article{Wasilewicz2022,
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.},
author = {Wasilewicz, Michał Andrzej},
journal = {Archivum Mathematicum},
keywords = {parabolic geometries; relative BGG conctruction; relative tractor calculus; Legendrean contact structures; Lagrangean contact structures; invariant differential operators; partial connections},
language = {eng},
number = {5},
pages = {339-347},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Elementary relative tractor calculus for Legendrean contact structures},
url = {http://eudml.org/doc/298904},
volume = {058},
year = {2022},
}

TY - JOUR
AU - Wasilewicz, Michał Andrzej
TI - Elementary relative tractor calculus for Legendrean contact structures
JO - Archivum Mathematicum
PY - 2022
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 058
IS - 5
SP - 339
EP - 347
AB - 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.
LA - eng
KW - parabolic geometries; relative BGG conctruction; relative tractor calculus; Legendrean contact structures; Lagrangean contact structures; invariant differential operators; partial connections
UR - http://eudml.org/doc/298904
ER -

References

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  1. Čap, A., Slovák, J., 10.1090/surv/154/03, Mathematical Surveys and Monographs, vol. 154, AMS, Providence, RI, 2009, Background and general theory. (2009) Zbl1183.53002MR2532439DOI10.1090/surv/154/03
  2. Čap, A., Souček, V., 10.1016/j.jalgebra.2016.06.007, J. Algebra 463 (2016), 188–210. (2016) MR3527545DOI10.1016/j.jalgebra.2016.06.007
  3. Čap, A., Souček, V., 10.1016/j.aim.2017.09.016, Adv. Math. 320 (2017), 1009–1062. (2017) MR3709128DOI10.1016/j.aim.2017.09.016
  4. Takeuchi, M., Legendrean contact structures on projective cotangent bundles, Osaka J. Math. 31 (4) (1994), 837–860. (1994) MR1315010

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