A Condition for Classical Elastic Curves on Surface

Authors : Ayşe ALTIN

Pages : 43-49

Doi:10.36753/mathenot.421755

View : 33 | Download : 13

Publication Date : 2018-04-27

Article Type : Research Paper

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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