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Bodies of Constant Width in Differential Geometry

  • Horst MartiniEmail author
  • Luis Montejano
  • Déborah Oliveros
Chapter

Abstract

Let \(\phi \subset \mathbb {E}^n\) be a strictly convex body whose boundary is twice differentiable and whose curvature never vanishes. Recall that the inverse Gauss map \(\gamma :\mathbb {S}^{n-1} \rightarrow {{\,\mathrm{\mathrm {bd}}\,}}\phi \) is a diffeomorphism that assigns to each unit vector \(u\in \mathbb {S}^{n-1}\) the point \(\gamma (u)\) in the boundary of \(\phi \) for which u is the outward unit normal vector.

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Horst Martini
    • 1
    Email author
  • Luis Montejano
    • 2
  • Déborah Oliveros
    • 2
  1. 1.Faculty of MathematicsChemnitz University of TechnologyChemnitzGermany
  2. 2.Instituto de MatemáticasUniversidad Nacional Autónoma de México, Campus JuriquillaQuerétaroMéxico

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