A Curvature Energy Problem on a Timelike Surface

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

References

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