On almost-Riemannian surfaces

Roberta Ghezzi[1]

  • [1] Department of Mathematical Sciences and Centre of Computational and Integrative Biology, Rutgers University Camden - Camden, 311 N 5th Street, Camden, NJ 08102, USA.

Séminaire de théorie spectrale et géométrie (2010-2011)

  • Volume: 29, page 15-49
  • ISSN: 1624-5458

Abstract

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An almost-Riemannian structure on a surface is a generalized Riemannian structure whose local orthonormal frames are given by Lie bracket generating pairs of vector fields that can become collinear. The distribution generated locally by orthonormal frames has maximal rank at almost every point of the surface, but in general it has rank 1 on a nonempty set which is generically a smooth curve. In this paper we provide a short introduction to 2-dimensional almost-Riemannian geometry highlighting its novelties with respect to Riemannian geometry. We present some results that investigate topological, metric and geometric aspects of almost-Riemannian surfaces from a local and global point of view.

How to cite

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Ghezzi, Roberta. "On almost-Riemannian surfaces." Séminaire de théorie spectrale et géométrie 29 (2010-2011): 15-49. <http://eudml.org/doc/219671>.

@article{Ghezzi2010-2011,
abstract = {An almost-Riemannian structure on a surface is a generalized Riemannian structure whose local orthonormal frames are given by Lie bracket generating pairs of vector fields that can become collinear. The distribution generated locally by orthonormal frames has maximal rank at almost every point of the surface, but in general it has rank 1 on a nonempty set which is generically a smooth curve. In this paper we provide a short introduction to 2-dimensional almost-Riemannian geometry highlighting its novelties with respect to Riemannian geometry. We present some results that investigate topological, metric and geometric aspects of almost-Riemannian surfaces from a local and global point of view.},
affiliation = {Department of Mathematical Sciences and Centre of Computational and Integrative Biology, Rutgers University Camden - Camden, 311 N 5th Street, Camden, NJ 08102, USA.},
author = {Ghezzi, Roberta},
journal = {Séminaire de théorie spectrale et géométrie},
keywords = {almost-Riemannian geometry; geodesics; Grushin plane; Lipschitz classification; Pontryagin maximum principle; Gauss-Bonnet formula},
language = {eng},
pages = {15-49},
publisher = {Institut Fourier},
title = {On almost-Riemannian surfaces},
url = {http://eudml.org/doc/219671},
volume = {29},
year = {2010-2011},
}

TY - JOUR
AU - Ghezzi, Roberta
TI - On almost-Riemannian surfaces
JO - Séminaire de théorie spectrale et géométrie
PY - 2010-2011
PB - Institut Fourier
VL - 29
SP - 15
EP - 49
AB - An almost-Riemannian structure on a surface is a generalized Riemannian structure whose local orthonormal frames are given by Lie bracket generating pairs of vector fields that can become collinear. The distribution generated locally by orthonormal frames has maximal rank at almost every point of the surface, but in general it has rank 1 on a nonempty set which is generically a smooth curve. In this paper we provide a short introduction to 2-dimensional almost-Riemannian geometry highlighting its novelties with respect to Riemannian geometry. We present some results that investigate topological, metric and geometric aspects of almost-Riemannian surfaces from a local and global point of view.
LA - eng
KW - almost-Riemannian geometry; geodesics; Grushin plane; Lipschitz classification; Pontryagin maximum principle; Gauss-Bonnet formula
UR - http://eudml.org/doc/219671
ER -

References

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