| Title:
|
A canonical connection on sub-Riemannian contact manifolds (English) |
| Author:
|
Eastwood, Michael |
| Author:
|
Neusser, Katharina |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
52 |
| Issue:
|
5 |
| Year:
|
2016 |
| Pages:
|
277-289 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We construct a canonically defined affine connection in sub-Riemannian contact geometry. Our method mimics that of the Levi-Civita connection in Riemannian geometry. We compare it with the Tanaka-Webster connection in the three-dimensional case. (English) |
| Keyword:
|
contact manifold |
| Keyword:
|
sub-Riemannian geometry |
| Keyword:
|
partial connection |
| Keyword:
|
pseudo-Hermitian geometry |
| MSC:
|
53C17 |
| MSC:
|
53D10 |
| MSC:
|
70G45 |
| idZBL:
|
Zbl 06674904 |
| idMR:
|
MR3610863 |
| DOI:
|
10.5817/AM2016-5-277 |
| . |
| Date available:
|
2016-12-20T21:54:42Z |
| Last updated:
|
2018-01-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/145935 |
| . |
| Reference:
|
[1] Agrachev, A.A., Barilari, D., Rizzi, L.: Sub-Riemannian curvature in contact geometry.to appear in J. Geom. Anal. |
| Reference:
|
[2] Agrachev, A.A., Zelenko, I.: Geometry of Jacobi curves I.J. Dynam. Control Systems 8 (1) (2002), 93–140. Zbl 1019.53038, MR 1874705, 10.1023/A:1013904801414 |
| Reference:
|
[3] Barilari, D., Rizzi, L.: On Jacobi fields and canonical connection in sub-Riemannian geometry.arXiv:1506.01827. |
| Reference:
|
[4] Bryant, R.L., Eastwood, M.G., Gover, A.R., Neusser, K.: Some differential complexes within and beyond parabolic geometry.arXiv:1112.2142. |
| Reference:
|
[5] Čap, A., Slovák, J.: Parabolic Geometries I: Background and General Theory.Surveys and Monographs, vol. 154, Amer. Math. Soc., 2009. Zbl 1183.53002, MR 2532439, 10.1090/surv/154 |
| Reference:
|
[6] Eastwood, M.G., Gover, A.R.: Prolongation on contact manifolds.Indiana Univ. Math. J. 60 (2011), 1425–1486. MR 2996997, 10.1512/iumj.2011.60.4980 |
| Reference:
|
[7] Falbel, E., Gorodski, C., Veloso, J.M.: Conformal sub-Riemannian geometry in dimension 3.Mat. Contemp. 9 (1995), 61–73. Zbl 0859.53021, MR 1378673 |
| Reference:
|
[8] Morimoto, T.: Cartan connection associated with a subriemannian structure.Differential Geom. Appl. 26 (2008), 75–78. Zbl 1147.53027, MR 2393974, 10.1016/j.difgeo.2007.12.002 |
| Reference:
|
[9] Rumin, M.: Un complexe de formes différentielles sur les variétés de contact.Comptes Rendus Acad. Sci. Paris Math. 310 (1990), 401–404. Zbl 0694.57010, MR 1046521 |
| Reference:
|
[10] Tanaka, N.: A differential geometric study on strongly pseudo-convex manifolds.Lectures in Mathematics, Kyoto University, Kinokuniya, 1975. Zbl 0331.53025, MR 0399517 |
| Reference:
|
[11] Webster, S.M.: Pseudo-Hermitian structures on a real hypersurface.J. Differential Geom. 13 (1978), 25–41. Zbl 0379.53016, MR 0520599, 10.4310/jdg/1214434345 |
| Reference:
|
[12] Zelenko, I., Li, C.: Differential geometry of curves in Lagrange Grassmannians with given Young diagram.Differential Geom. Appl. 27 (2009), 723–742. Zbl 1177.53020, MR 2552681, 10.1016/j.difgeo.2009.07.002 |
| . |
