A Note on Inextensible Flows of Curves on Oriented Surface

In this paper, the general formulation for inextensible flows of curves on oriented surface in \(\mathbb{R}^3 \) is investigated. The necessary and sufficient conditions for inextensible curve flow lying an oriented surface are expressed as a partial differential equation involving the geodesic curv...

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Bibliographic Details
Published in:arXiv.org 2011-06
Main Authors: Yildiz, Onder Gokmen, Soley Ersoy, Masal, Melek
Format: Article
Language:English
Subjects:
Curvature
Partial differential equations
Online Access:Get full text
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Summary:In this paper, the general formulation for inextensible flows of curves on oriented surface in \(\mathbb{R}^3 \) is investigated. The necessary and sufficient conditions for inextensible curve flow lying an oriented surface are expressed as a partial differential equation involving the geodesic curvature and the geodesic torsion. Moreover, some special cases of inextensible curves on oriented surface are given.
ISSN:2331-8422
DOI:10.48550/arxiv.1106.2012