On the total absolute curvature of closed curves in spheres (Q1074118)
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scientific article; zbMATH DE number 3947068
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the total absolute curvature of closed curves in spheres |
scientific article; zbMATH DE number 3947068 |
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On the total absolute curvature of closed curves in spheres (English)
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1986
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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.
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total absolute curvature
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level functions
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critical points
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spherical curves
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