Evolutes and isoperimetric deficit in two-dimensional spaces of constant curvature

Julià Cufí; Agustí Reventós

doi:10.5817/AM2014-4-219

Evolutes and isoperimetric deficit in two-dimensional spaces of constant curvature

Julià Cufí, Agustí Reventós

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Abstract

© 2014, Masarykova Universita. All rights reserved. We relate the total curvature and the isoperimetric deficit of a curve γ in a two-dimensional space of constant curvature with the area enclosed by the evolute of γ. We provide also a Gauss-Bonnet theorem for a special class of evolutes.

Original language	English
Pages (from-to)	219-236
Journal	Archivum Mathematicum
Volume	50
Issue number	4
DOIs	https://doi.org/10.5817/AM2014-4-219
Publication status	Published - 1 Jan 2014

Keywords

Curvature
Evolutes
Gauss-Bonnet
Isoperimetric deficit

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abstract = "{\textcopyright} 2014, Masarykova Universita. All rights reserved. We relate the total curvature and the isoperimetric deficit of a curve γ in a two-dimensional space of constant curvature with the area enclosed by the evolute of γ. We provide also a Gauss-Bonnet theorem for a special class of evolutes.",

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AU - Reventós, Agustí

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N2 - © 2014, Masarykova Universita. All rights reserved. We relate the total curvature and the isoperimetric deficit of a curve γ in a two-dimensional space of constant curvature with the area enclosed by the evolute of γ. We provide also a Gauss-Bonnet theorem for a special class of evolutes.

AB - © 2014, Masarykova Universita. All rights reserved. We relate the total curvature and the isoperimetric deficit of a curve γ in a two-dimensional space of constant curvature with the area enclosed by the evolute of γ. We provide also a Gauss-Bonnet theorem for a special class of evolutes.

KW - Curvature

KW - Evolutes

KW - Gauss-Bonnet

KW - Isoperimetric deficit

U2 - 10.5817/AM2014-4-219

DO - 10.5817/AM2014-4-219

M3 - Article

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VL - 50

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EP - 236

JO - Archivum Mathematicum

JF - Archivum Mathematicum

IS - 4

ER -

Evolutes and isoperimetric deficit in two-dimensional spaces of constant curvature

Abstract

Keywords

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