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 E-4. First, we determine locally all parallel normalized mean curvature vector (PNMCV) biconservative surfaces in E-4, showing that they are certain rotational surfaces. Then, we consider meridian surfaces lying on a rotational hypersurface of E-4 and construct a family of biconservative surfaces with flat normal bundle and non-parallel normalized mean curvature vector. (C) 2017 Elsevier Inc. All rights reserved.