In this paper, we construct and classify minimal surfaces foliated byhorizontal constant curvature curves in product manifolds $M \times \R$, where$M$ is the hyperbolic plane, the Euclidean plane or the two dimensional sphere.The main tool is the existence of a Jacobi field which characterize theproperty to be foliated in circles and geodesics in these product manifolds. Itis related to harmonic maps.
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机译：在本文中，我们构造和分类了由产品流形$ M \ times \ R $中水平恒定曲率曲线形成的最小曲面，其中$ M $是双曲平面，欧几里德平面或二维球面，主要工具是存在性Jacobi场的特征，其特征是在这些产品流形中以圆和测地线叶的属性。它与谐波图有关。
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