Homotopies using conformal transformation with invariant total normal twist

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>...

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Main Authors: El-Said R. Lashin, Tarek F. Mersal
Format: Article
Language:English
Published: Università degli Studi di Catania 1999-10-01
Series:Le Matematiche
Online Access:http://www.dmi.unict.it/ojs/index.php/lematematiche/article/view/326
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spelling doaj-676f2c1b8c404f48b5aa7d53c4e7337f2020-11-25T01:24:14ZengUniversità degli Studi di CataniaLe Matematiche0373-35052037-52981999-10-01542221227302Homotopies using conformal transformation with invariant total normal twistEl-Said R. LashinTarek F. MersalThe 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 />http://www.dmi.unict.it/ojs/index.php/lematematiche/article/view/326
collection DOAJ
language English
format Article
sources DOAJ
author El-Said R. Lashin
Tarek F. Mersal
spellingShingle El-Said R. Lashin
Tarek F. Mersal
Homotopies using conformal transformation with invariant total normal twist
Le Matematiche
author_facet El-Said R. Lashin
Tarek F. Mersal
author_sort El-Said R. Lashin
title Homotopies using conformal transformation with invariant total normal twist
title_short Homotopies using conformal transformation with invariant total normal twist
title_full Homotopies using conformal transformation with invariant total normal twist
title_fullStr Homotopies using conformal transformation with invariant total normal twist
title_full_unstemmed Homotopies using conformal transformation with invariant total normal twist
title_sort homotopies using conformal transformation with invariant total normal twist
publisher Università degli Studi di Catania
series Le Matematiche
issn 0373-3505
2037-5298
publishDate 1999-10-01
description 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 />
url http://www.dmi.unict.it/ojs/index.php/lematematiche/article/view/326
work_keys_str_mv AT elsaidrlashin homotopiesusingconformaltransformationwithinvarianttotalnormaltwist
AT tarekfmersal homotopiesusingconformaltransformationwithinvarianttotalnormaltwist
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