A Condition for Classical Elastic Curves on Surface

Year 2018, , 43 - 49, 27.04.2018

Ayşe Altın

https://doi.org/10.36753/mathenot.421755

Abstract

In this paper, we consider two fixed points p to q on a Riemannian surface M in 3-dimensional Euclidean
space. We obtain a condition for classical elastic curves with in the family of all curves from p to q on M.
We also prove that this condition can be expressed in terms of the curvature functions. The condition is
realized for curves whose geodesic and normal curvature functions are both constant. 

Keywords

Energy, Energy of a unit vector field, Elastica

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