Minimal surfaces of Riemann type in three-dimensional product manifolds

Laurent Hauswirth (1)

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées

In this paper, we construct and classify minimal surfaces foliated by horizontal constant curvature curves in MxR, where M is H^2, R^2 or S^2. The main tool is the existence of a so called "Shiffman" Jacobi field which characterize the property to be foliated in circles in these product manifolds.

Domaines: Géométrie différentielle [math.DG]

Laurent Hauswirth. Minimal surfaces of Riemann type in three-dimensional product manifolds. Pacif Journal of Math, 2006, 224 (1), pp.91-117. ⟨hal-00796841⟩