On biconservative surfaces in 3-dimensional space forms

TL;DR

This paper studies biconservative surfaces in 3D space forms with positive mean curvature, providing a new intrinsic characterization and relating them to Ricci surfaces through a specific Riemannian metric.

Contribution

It introduces a Riemannian metric making biconservative surfaces Ricci surfaces and offers an intrinsic characterization of these surfaces.

Findings

Established a Riemannian metric $g_r$ on biconservative surfaces

Showed $ ext{(M, g_r)}$ is a Ricci surface in $N^3(c)$

Provided an intrinsic characterization of biconservative surfaces

Abstract

We consider biconservative surfaces $\left(M^2,g\right)$ in a space form $N^3(c)$, with mean curvature function $f$ satisfying $f>0$ 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.