We explicitly classify the nonharmonic biharmonic submanifolds of the unit threedimensional sphere S 3 .

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We introduce the notion of biconservative hypersurfaces, that is hypersurfaces with conservative stress-energy tensor with respect to the bienergy. We give the (local) classification of biconservative surfaces in three-dimensional space forms

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 threedimensional Lie group Sol. We also classify, using a geometric method, the biharmonic curves of the three-dimensional Cartan-Vranceanu manifolds.2000 Mathematics Subject Classification. 58E20.

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