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1 - Geometry of Surfaces in R3

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 preliminary chapter we study the geometry ofsmooth two-dimensional surfaces in $\mathbb{R}^3$ asa “warm-up problem” and we recover some classicalresults. In the fist part of the chapter we considersurfaces in $\mathbb{R}^3$ endowed with the standardEuclidean product. In the second part we studysurfaces in the 3D pseudo-Euclidean space, that is$\mathbb{R}^3$ endowed with a sign-indefinite innerproduct.

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Publisher: Cambridge University Press
Print publication year: 2019

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  • Geometry of Surfaces in R3
  • 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/10.1017/9781108677325.003
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  • Geometry of Surfaces in R3
  • 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/10.1017/9781108677325.003
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.

  • Geometry of Surfaces in R3
  • 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/10.1017/9781108677325.003
Available formats
×