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1 results

  • 1 - 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
    Published online:
    28 October 2019
    Print publication:
    31 October 2019, pp 11-44

  • 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.