On the uniqueness of complete biconservative surfaces in $3$-dimensional space forms

Abstract

Biconservative surfaces are surfaces with divergence-free stress-bienergy tensor. Simply connected, complete, non-$CMC$ biconservative surfaces in $3$-dimensional space forms were constructed working in extrinsic and intrinsic ways. Then, one raises the question of the uniqueness of such surfaces. In this paper we give a positive answer to this question.

18 pages, 1 figure. We changed the title, abstract and introduction, and we added a new section. arXiv admin note: text overlap with arXiv:1909.12709