Minimal surfaces of riemann type in three-dimensional product manifolds

Abstract

We construct and classify minimal surfaces foliated by horizontal curves of constant curvature in ℍ2×ℝ, ℝ2×ℝ and S{double-struck}2×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.