The Classical Elastic Curves in A 3-Dimensional Indefinite-Riemannian Manifold


	Journal of Applied Sciences
	Year: 2012 \| Volume: 12 \| Issue: 12 \| Page No.: 1303-1307 DOI: 10.3923/jas.2012.1303.1307

The Classical Elastic Curves in A 3-Dimensional Indefinite-Riemannian Manifold

Nemat Abazari and Yusuf Yayli

Abstract: In this study the mathematical idealization of the classical variational problem in 3-dimensional indefinite-Riemannian Manifolds is studied for the curve α which is timelike and spacelike, parameterized by the arc-length. The geodesic curvature and torsion of an elastic curve are evaluated if they exist as the solutions of the differential equations for all different cases. Due to elastic curve definition, the minimum principle theorem is applied to elastic energy function which is defined as the integral of the squared geodesic curvature of the curve.

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How to cite this article:

Nemat Abazari and Yusuf Yayli, 2012. The Classical Elastic Curves in A 3-Dimensional Indefinite-Riemannian Manifold. Journal of Applied Sciences, 12: 1303-1307.

DOI: 10.3923/jas.2012.1303.1307

URL: https://scialert.net/abstract/?doi=jas.2012.1303.1307

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