# On biconservative surfaces in Euclidean spaces

## TL;DR

This paper classifies biconservative surfaces with parallel normalized mean curvature vector in four-dimensional Euclidean space, providing a complete local classification and an example of such surfaces' existence.

## Contribution

It offers the first complete local classification of biconservative PNMCV surfaces in 4 and demonstrates their existence through explicit examples.

## Key findings

- Complete local classification of biconservative PNMCV surfaces in 4
- Existence of PNMCV biconservative surfaces in 4 shown by example
- New insights into the geometry of biconservative surfaces in higher dimensions

## 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 $\mathbb{E}^4$.