On biconservative surfaces in 4-dimensional Euclidean space

Abstract

In this paper, we study non-CMC biconservative surfaces with flat normal bundle in the Euclidean 4-space E4. First, we determine locally all parallel normalized mean curvature vector (PNMCV) biconservative surfaces in E4, showing that they are certain rotational surfaces. Then, we consider meridian surfaces lying on a rotational hypersurface of E4 and construct a family of biconservative surfaces with flat normal bundle and non-parallel normalized mean curvature vector.