Abstract
In this paper, we construct a new method for inextensible flows of curves in E³. Using the Frenet frame of the given curve, we present partial differential equations. We give some characterizations for curvatures of a curve in E³.
Highlights
To meet the requirements here, the basic elements of the theory of curves in the space E3 are briefly presented; a more complete elementary treatment can be found in [8]
Denote by {T, N, B} the moving Frenet-Serret frame along the curve α in the space E3
For an arbitrary curve α with first and second curvature, κ and τ in the space E3, the following Frenet-Serret formulae are given in [8] written under matrix form
Summary
To meet the requirements here, the basic elements of the theory of curves in the space E3 are briefly presented; a more complete elementary treatment can be found in [8]. Let α = α(s) be a regular curve in E3. Denote by {T, N, B} the moving Frenet-Serret frame along the curve α in the space E3. For an arbitrary curve α with first and second curvature, κ and τ in the space E3, the following Frenet-Serret formulae are given in [8] written under matrix form
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