On biconservative surfaces in Euclidean spaces

Abstract

In this paper, we study biconservative surfaces with parallel normalized mean curvature vector in ${\mathbb{E}}^4$. We obtain complete local classification in ${\mathbb{E}}^4$ for a biconservative PNMCV surface. We also give an example to show the existence of PNMCV biconservative surfaces in ${\mathbb{E}}^4$.