Journal of Applied Sciences1812-56541812-5662Asian Network for Scientific Information10.3923/jas.2012.1303.1307AbazariNematYayliYusuf1220121212In 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.]]>Love, A.E.H.,1927Hsu, M.H.,2007Yanti, P.A.A. and T.M. Mahlia,2009Akanmu, A.A. and A.H. Gambo,2007Akanmu, A.A. and A.H. Gambo,2008Langer, J. and D.A. Singer,19843.]]>Koiso, N.,1992Fernandez, A., J. Guerreo, M.A. Javaloyes and P. Lucas,2006Barros, M., O.J. Garay and D.A. Singer,1999Singer, D.A.,2007Sager, I., N. Abazari, E. Ekmekci and Y. Yayli,2011Lopez, R.,2008Koklu, K.,2002Davis, H.T.,1962Jing-Lei, G. and W. Zhi-Jian,2011Abazari, R.,2011