Communications in Analysis and Geometry

Volume 24 (2016)

Number 5

On biconservative surfaces in $3$-dimensional space forms

Pages: 1027 – 1045

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

Authors

Dorel Fetcu (Department of Mathematics and Informatics, Gh. Asachi Technical University, Iasi, Romania)

Simona Nistor (Faculty of Mathematics, Cuza University of Iasi, Romania)

Cezar Oniciuc (Faculty of Mathematics, Cuza University of Iasi, Romania)

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

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