The total absolute curvature of open curves in \(E^{3}\)

zbMath1202.53003MaRDI QIDQ1022560

Jin-ichi Itoh, Robert Sinclair, Kazuyuki Enomoto

Publication date: 22 June 2009

Published in: Illinois Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.ijm/1242414121

zbMATH Keywords

convex curvetotal absolute curvaturelimit curveopen curvepiecewise linear curve

Mathematics Subject Classification ID

Curves in Euclidean and related spaces (53A04)

Related Items (4)

The total absolute curvature and the total absolute torsion of open curves in the Euclidean spaces ⋮ The total mixed curvature of open curves in \(E^3\) ⋮ The total squared curvature of curves and approximation by piecewise circular curves ⋮ The weak Frenet frame of non-smooth curves with finite total curvature and absolute torsion

Uses Software

• Thaw

Cites Work

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• Circular billiard tables, conjugate loci, and a cardioid
• The cut loci and the conjugate loci on ellipsoids
• The total absolute curvature of nonclosed curves in \(S^2\)
• The total absolute curvature of nonclosed curves in \(S^2\). II
• The cut locus of a two-sphere of revolution and Toponogov's comparison theorem
• On the total curvature of knots
• The influence of elasticity on analysis: The classic heritage
• Thaw: A Tool for Approximating Cut Loci on a Triangulation of a Surface
• On total curvatures of closed space curves

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