Document Zbl 1340.53004

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Cufí, Julià; Reventós, Agustí

Evolutes and isoperimetric deficit in two-dimensional spaces of constant curvature. (English) Zbl 1340.53004

Arch. Math., Brno 50, No. 4, 219-236 (2014).

The total curvature and the isoperimetric deficit of a curve \( \gamma \) in a two-dimensional space of constant curvature is related with the area enclosed by the evolute of the curve \( \gamma \). The Gauss-Bonnet theorem for a special class of evolutes is proved.

Reviewer: Josef Janyška (Brno)

Cited in 1 Document

MSC:

53A04	Curves in Euclidean and related spaces
52A55	Spherical and hyperbolic convexity
52A10	Convex sets in \(2\) dimensions (including convex curves)

Keywords:

curvature; evolutes; isoperimetric deficit; Gauss-Bonnet

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