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10 - Nonholonomic Tangent Space

Published online by Cambridge University Press:  28 October 2019

Andrei Agrachev
Affiliation:
Scuola Internazionale Superiore di Studi Avanzati, Trieste
Davide Barilari
Affiliation:
Université de Paris VII (Denis Diderot)
Ugo Boscain
Affiliation:
Centre National de la Recherche Scientifique (CNRS), Paris
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Summary

In this chapter we introduce the notion of anonholomonic tangent space, which can be regarded asthe “principal part” of the structure defined on amanifold by the distribution in a neighborhood of apoint. We give an intrinsic construction through thetheory of jets of curves and the notion of smoothadmissible variation. Also, we discuss the Ball–Boxtheorem, and a classification of nonholonomictangent spaces in low dimensions.

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Publisher: Cambridge University Press
Print publication year: 2019

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  • Nonholonomic Tangent Space
  • Andrei Agrachev, Scuola Internazionale Superiore di Studi Avanzati, Trieste, Davide Barilari, Université de Paris VII (Denis Diderot), Ugo Boscain, Centre National de la Recherche Scientifique (CNRS), Paris
  • Book: A Comprehensive Introduction to Sub-Riemannian Geometry
  • Online publication: 28 October 2019
  • Chapter DOI: https://doi.org/10.1017/9781108677325.012
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  • Nonholonomic Tangent Space
  • Andrei Agrachev, Scuola Internazionale Superiore di Studi Avanzati, Trieste, Davide Barilari, Université de Paris VII (Denis Diderot), Ugo Boscain, Centre National de la Recherche Scientifique (CNRS), Paris
  • Book: A Comprehensive Introduction to Sub-Riemannian Geometry
  • Online publication: 28 October 2019
  • Chapter DOI: https://doi.org/10.1017/9781108677325.012
Available formats
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Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Nonholonomic Tangent Space
  • Andrei Agrachev, Scuola Internazionale Superiore di Studi Avanzati, Trieste, Davide Barilari, Université de Paris VII (Denis Diderot), Ugo Boscain, Centre National de la Recherche Scientifique (CNRS), Paris
  • Book: A Comprehensive Introduction to Sub-Riemannian Geometry
  • Online publication: 28 October 2019
  • Chapter DOI: https://doi.org/10.1017/9781108677325.012
Available formats
×