Bodies of Constant Width in Differential Geometry

Horst Martini (), Luis Montejano and Déborah Oliveros
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Horst Martini: Chemnitz University of Technology, Faculty of Mathematics
Luis Montejano: Universidad Nacional Autónoma de México, Campus Juriquilla, Instituto de Matemáticas
Déborah Oliveros: Universidad Nacional Autónoma de México, Campus Juriquilla, Instituto de Matemáticas

Chapter Chapter 11 in Bodies of Constant Width, 2019, pp 247-277 from Springer

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

Date: 2019
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DOI: 10.1007/978-3-030-03868-7_11

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