On Jacobi fields and a canonical connection in sub-Riemannian geometry
Archivum Mathematicum (2017)
- Volume: 053, Issue: 2, page 77-92
- ISSN: 0044-8753
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topBarilari, Davide, and Rizzi, Luca. "On Jacobi fields and a canonical connection in sub-Riemannian geometry." Archivum Mathematicum 053.2 (2017): 77-92. <http://eudml.org/doc/288210>.
@article{Barilari2017,
abstract = {In sub-Riemannian geometry the coefficients of the Jacobi equation define curvature-like invariants. We show that these coefficients can be interpreted as the curvature of a canonical Ehresmann connection associated to the metric, first introduced in [15]. We show why this connection is naturally nonlinear, and we discuss some of its properties.},
author = {Barilari, Davide, Rizzi, Luca},
journal = {Archivum Mathematicum},
keywords = {sub-Riemannian geometry; curvature; connection; Jacobi fields},
language = {eng},
number = {2},
pages = {77-92},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {On Jacobi fields and a canonical connection in sub-Riemannian geometry},
url = {http://eudml.org/doc/288210},
volume = {053},
year = {2017},
}
TY - JOUR
AU - Barilari, Davide
AU - Rizzi, Luca
TI - On Jacobi fields and a canonical connection in sub-Riemannian geometry
JO - Archivum Mathematicum
PY - 2017
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 053
IS - 2
SP - 77
EP - 92
AB - In sub-Riemannian geometry the coefficients of the Jacobi equation define curvature-like invariants. We show that these coefficients can be interpreted as the curvature of a canonical Ehresmann connection associated to the metric, first introduced in [15]. We show why this connection is naturally nonlinear, and we discuss some of its properties.
LA - eng
KW - sub-Riemannian geometry; curvature; connection; Jacobi fields
UR - http://eudml.org/doc/288210
ER -
References
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