Generalized Riemann minimal surfaces examples in three-dimensional manifolds products

2005/07/08 by Laurent Hauswirth, L. Hauswirth, Hauswirth, L.
Mathematics · #Classical Analysis and ODEs (math.CA) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Point processes and geometric inequalities #math.CA #math.DG

paper · pdf · doi:10.48550/arxiv.math/0507187

23 pages, 8 figures

arxiv created 2005/07/08 · openalex publication_date 2005/07/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we construct and classify minimal surfaces foliated by horizontal constant curvature curves in product manifolds M × \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 the property to be foliated in circles and geodesics in these product manifolds. It is related to harmonic maps.

Related

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• Minimal surfaces in the Riemannian product of surfaces
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• Special Weingarten surfaces foliated by circles