Communications in Analysis and Geometry
Volume 24 (2016)
On biconservative surfaces in $3$-dimensional space forms
Pages: 1027 – 1045
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.
biconservative surfaces, minimal surfaces, real space forms
2010 Mathematics Subject Classification