| 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:
|
http://hdl.handle.net/10338.dmlcz/151158 |
| . |
| 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 |
| . |
