A note on inextensible flows of curves in Een
\"Onder G\"okmen Y{\i}ld{\i}z, Murat Tosun, S{\i}dd{\i}ka \"O., Karaku\c{s}
TL;DR
This paper formulates the conditions for inextensible flows of curves in Euclidean space using partial differential equations involving curvature, providing a mathematical framework for understanding such flows.
Contribution
It introduces a general formulation and necessary conditions for inextensible curve flows in Euclidean space, expressed as PDEs involving curvature.
Findings
Derived necessary and sufficient conditions for inextensible flows
Expressed conditions as PDEs involving curvature
Provides a mathematical framework for inextensible flows
Abstract
In this paper, we investigate the general formulation for inextensible flows of curves in En. The necessary and sufficient conditions for inextensible curve flow are expressed as a partial differential equation involving the curvatures.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometry and complex manifolds · Mathematical Dynamics and Fractals