On the total absolute curvature of closed curves in spheres
type: Item
instance of: scholarly article
title: On the total absolute curvature of closed curves in spheres
zbMATH Open document ID: 0589.53001
DOI: 10.1007/BF01172493
author: Eberhard Teufel
published in: Manuscripta Mathematica
publication date: 1986-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/155187
review text: The total absolute curvature (tac) of a closed curve in a Euclidean space satisfies Fenchel's resp. Fary-Milnor's inequality. This article treats tac of closed curves in spheres. We derive similar inequalities depending on the length of the curve resp. the area of surfaces of disk-type bounded by the curve. The proof starts from the computation of tac as mean value of the number of critical points of certain level functions [see the author's article, ibid. 31, 119-147 (1980; Zbl 0429.53038)] uses some topological considerations and Poincaré's integral geometric formula for the computation of length resp. area.
Mathematics Subject Classification ID: 53A04
Mathematics Subject Classification ID: 53C65
Mathematics Subject Classification ID: 53A35
zbMATH DE Number: 3947068
zbMATH Keywords: total absolute curvature
zbMATH Keywords: level functions
zbMATH Keywords: critical points
zbMATH Keywords: spherical curves
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3947068