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# Communications in Analysis and Geometry

## Volume 24 (2016)

### Number 5

### On biconservative surfaces in $3$-dimensional space forms

Pages: 1027 – 1045

DOI: https://dx.doi.org/10.4310/CAG.2016.v24.n5.a5

#### Authors

#### Abstract

We consider biconservative surfaces $\left ( M^2, g \right )$ in a space form $N^3(c)$, with mean curvature function $f$ satisfying $f \gt 0$ and $\nabla f \neq 0$ at any point, and determine a certain Riemannian metric $g_r$ on $M$ such that $\left ( M^2, g_r \right )$ is a Ricci surface in $N^3(c)$. We also obtain an intrinsic characterization of these biconservative surfaces.

#### Keywords

biconservative surfaces, minimal surfaces, real space forms

#### 2010 Mathematics Subject Classification

53A10, 53C42

Published 6 March 2017