A canonical connection on sub-Riemannian contact manifolds
Michael Eastwood; Katharina Neusser
Archivum Mathematicum (2016)
- Volume: 052, Issue: 5, page 277-289
- ISSN: 0044-8753
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topEastwood, Michael, and Neusser, Katharina. "A canonical connection on sub-Riemannian contact manifolds." Archivum Mathematicum 052.5 (2016): 277-289. <http://eudml.org/doc/287563>.
@article{Eastwood2016,
abstract = {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.},
author = {Eastwood, Michael, Neusser, Katharina},
journal = {Archivum Mathematicum},
keywords = {contact manifold; sub-Riemannian geometry; partial connection; pseudo-Hermitian geometry},
language = {eng},
number = {5},
pages = {277-289},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {A canonical connection on sub-Riemannian contact manifolds},
url = {http://eudml.org/doc/287563},
volume = {052},
year = {2016},
}
TY - JOUR
AU - Eastwood, Michael
AU - Neusser, Katharina
TI - A canonical connection on sub-Riemannian contact manifolds
JO - Archivum Mathematicum
PY - 2016
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 052
IS - 5
SP - 277
EP - 289
AB - 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.
LA - eng
KW - contact manifold; sub-Riemannian geometry; partial connection; pseudo-Hermitian geometry
UR - http://eudml.org/doc/287563
ER -
References
top- Agrachev, A.A., Barilari, D., Rizzi, L., Sub-Riemannian curvature in contact geometry, to appear in J. Geom. Anal.
- Agrachev, A.A., Zelenko, I., 10.1023/A:1013904801414, J. Dynam. Control Systems 8 (1) (2002), 93–140. (2002) Zbl1019.53038MR1874705DOI10.1023/A:1013904801414
- Barilari, D., Rizzi, L., On Jacobi fields and canonical connection in sub-Riemannian geometry, arXiv:1506.01827.
- Bryant, R.L., Eastwood, M.G., Gover, A.R., Neusser, K., Some differential complexes within and beyond parabolic geometry, arXiv:1112.2142.
- Čap, A., Slovák, J., 10.1090/surv/154, Surveys and Monographs, vol. 154, Amer. Math. Soc., 2009. (2009) Zbl1183.53002MR2532439DOI10.1090/surv/154
- Eastwood, M.G., Gover, A.R., 10.1512/iumj.2011.60.4980, Indiana Univ. Math. J. 60 (2011), 1425–1486. (2011) MR2996997DOI10.1512/iumj.2011.60.4980
- Falbel, E., Gorodski, C., Veloso, J.M., Conformal sub-Riemannian geometry in dimension 3, Mat. Contemp. 9 (1995), 61–73. (1995) Zbl0859.53021MR1378673
- Morimoto, T., 10.1016/j.difgeo.2007.12.002, Differential Geom. Appl. 26 (2008), 75–78. (2008) Zbl1147.53027MR2393974DOI10.1016/j.difgeo.2007.12.002
- Rumin, M., Un complexe de formes différentielles sur les variétés de contact, Comptes Rendus Acad. Sci. Paris Math. 310 (1990), 401–404. (1990) Zbl0694.57010MR1046521
- Tanaka, N., A differential geometric study on strongly pseudo-convex manifolds, Lectures in Mathematics, Kyoto University, Kinokuniya, 1975. (1975) Zbl0331.53025MR0399517
- Webster, S.M., 10.4310/jdg/1214434345, J. Differential Geom. 13 (1978), 25–41. (1978) Zbl0379.53016MR0520599DOI10.4310/jdg/1214434345
- Zelenko, I., Li, C., 10.1016/j.difgeo.2009.07.002, Differential Geom. Appl. 27 (2009), 723–742. (2009) Zbl1177.53020MR2552681DOI10.1016/j.difgeo.2009.07.002
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