The Euler-Lagrange Method for Biharmonic Curves

In this article we consider the Euler-Lagrange method associated to a suitable bilagrangian to study biharmonic curves of a Riemannian manifold. We apply this method to characterize biharmonic curves of the three-dimensional Lie group Sol. We also classify, using a geometric method, the biharmonic curves of the three-dimensional Cartan-Vranceanu manifolds. Dedicated to the memory of Professor Aldo Cossu Work partially supported by GNSAGA (Italy); the third author was supported by a CNR-NATO fellowship (Italy), and by the Grant At, 191/2006, CNCSIS (Romania).