A Condition for Classical Elastic Curves on Surface

Yıl 2018, Cilt: 6 Sayı: 1, 43 - 49, 27.04.2018

Ayşe Altın

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

Öz

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. 

Anahtar Kelimeler

Energy, Energy of a unit vector field, Elastica

Kaynakça

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