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arXiv · 1806.03980

Relaxed Elastic Line On An Oriented Surface In The Galilean Space

Tevfik Şahin
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Abstract

In this paper, we consider the classical variational problem in the Galilean space. we develop the Euler-Lagrange equations for a elastic line on an oriented surface in the Galilean 3-dimensional space $G_3$. Using the varia- tion method, we will try to give some characterization for the solution curve (the elastic line) of energy equation described by the total squared curvature function of a curve on an oriented surface in $G_3$. Finally, we will investigate whether or not the relaxed elastic curves are on a geodesic.

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Tevfik Şahin. 2018-06-06. Relaxed Elastic Line On An Oriented Surface In The Galilean Space. https://arxiv.org/abs/1806.03980

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