Vol. 224, No. 1, 2006

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ISSN: 0030-8730
Minimal surfaces of Riemann type in three-dimensional product manifolds

Laurent Hauswirth

Vol. 224 (2006), No. 1, 91–117
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
Authors
Laurent Hauswirth
Université de Marne-la-Vallée
5, cité Descartes
Champs-sur-Marne
77454 Marne-la-Vallée
France