Biconservative surfaces
  In this work we obtain some geometric properties of biconservative surfaces into a Riemannian manifold. In particular, we shall study the relationship between biconservative surfaces and the holomorphicity of a generalized Hopf function. Also, we give a complete classification of CMC biconservative surfaces in a $4$-dimensional space form. 
S. Montaldo, C. Oniciuc, A. Ratto
math.DG