A Curvature Energy Problem on a Timelike Surface

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International Electronic Journal of Geometry
Volume:11 Issue:2
A Curvature Energy Problem on a Timelike Surface

A Curvature Energy Problem on a Timelike Surface

Authors : Gözde Özkan TÜKEL, Ahmet YÜCESAN

Pages : 120-125

Doi:10.36890/iejg.545141

View : 35 | Download : 7

Publication Date : 2018-11-30

Article Type : Research Paper

Abstract :We present a variational study of finding null relaxed elastic lines which are extremals of a geometric energy functional, subject to suitable constraints and boundary conditions on a timelike surface in Minkowski 3-space. We derive an Euler-Lagrange equation for a null relaxed elastic line with regard to geodesic curvature, geodesic torsion and normal curvature of the curve on the timelike surface. Finally, we give some examples for null relaxed elastic lines on the pseudo-sphere and pseudo-cylinder.
Keywords : Null relaxed elastic line, Euler Lagrange equation, variational calculus

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