Homotopies using conformal transformation with invariant total normal twist
The aim of this paper is to detect a homotopy to a spherical curve with invariant total normal twist 0. Also, we use conformal transformation to prove a theorem that for any immersed closed <em>C^</em><em>3</em> -curve c in the Euclidean <em>3</em>-space <em>...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Università degli Studi di Catania
1999-10-01
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| Series: | Le Matematiche |
| Online Access: | http://www.dmi.unict.it/ojs/index.php/lematematiche/article/view/326 |
| Summary: | The aim of this paper is to detect a homotopy to a spherical curve with invariant total normal twist 0. Also, we use conformal transformation to prove a theorem that for any immersed closed <em>C^</em><em>3</em> -curve c in the Euclidean <em>3</em>-space <em>E^3</em> with vanishing total normal twist, there exists a Frenet curve <em>ĉ</em> homotopic to <em>c</em> in an arbitrary neighborhood of <em>c</em> such that the total normal twist is invariant along the homotopy between <em>c</em> and <em>ĉ</em> in that neighborhood.<br /> |
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| ISSN: | 0373-3505 2037-5298 |