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.
We study some aspect of the left-invariant Riemannian geometry on a class of nilpotent Lie groups H{p, r) that generalize the Heisenberg group H2p+\. Let us prove that the groups of type H (or Kaplan's spaces) and the H{p, r) groups have same common Riemannian properties but they are not the same spaces.
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