- Mathematical Sciences and Applications E-Notes
- Vol: 6 Issue: 1
- A Condition for Classical Elastic Curves on Surface
A Condition for Classical Elastic Curves on Surface
Authors : Ayşe ALTIN
Pages : 43-49
Doi:10.36753/mathenot.421755
View : 6 | Download : 4
Publication Date : 2018-04-27
Article Type : Research
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