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Surfaces in three-dimensional space forms with divergence-free stress-bienergy tensor. (English) Zbl 1294.53006
The authors introduce the notion of biconservative surfaces. They first find the PDE that satisfies the mean curvature function of a biconservative surface in a three dimensional space form. Then, the paper is devoted to the local classification of biconservative surfaces in three dimensional space forms. This is done in three sections in which they examine separately the cases of surfaces in the Euclidean space, in the sphere and in the hyperbolic space.

##### MSC:
 53A05 Surfaces in Euclidean and related spaces 53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) 49Q10 Optimization of shapes other than minimal surfaces
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