Minimal surfaces of Riemann type in three-dimensional product manifolds

Laurent Hauswirth

Vol. 224 (2006), No. 1, 91–117

DOI: 10.2140/pjm.2006.224.91

Abstract

We construct and classify minimal surfaces foliated by horizontal curves of constant curvature in ℍ²×ℝ, ℝ²×ℝ and 𝕊²×ℝ. The main tool is the existence of a Shiffman Jacobi field; such fields characterize the property of being foliated by circles in these product manifolds.

Keywords

periodic minimal surface, harmonic map, stable minimal surface, stability index, Jacobi field, Jacobi operator

Mathematical Subject Classification 2000

Primary: 49Q05, 53C42, 53A10, 57R40, 53C43, 58E20

Milestones

Received: 2 July 2004

Revised: 31 January 2005

Accepted: 9 June 2005

Published: 1 March 2006