Surfaces in three-dimensional space forms with divergence-free   stress-bienergy tensor
  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 3-dimensional space forms. 
R. Caddeo, S. Montaldo, C. Oniciuc, P. Piu
math.DG