Generalized Riemann minimal surfaces examples in three-dimensional manifolds products

In this paper, we construct and classify minimal surfaces foliated by horizontal 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...

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Bibliographic Details
Published in:arXiv.org 2005-07
Main Author: Hauswirth, L
Format: Article
Language:English
Subjects:
Curvature
Euclidean geometry
Geodesy
Manifolds (mathematics)
Minimal surfaces
Online Access:Get full text
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Summary:In this paper, we construct and classify minimal surfaces foliated by horizontal 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 the property to be foliated in circles and geodesics in these product manifolds. It is related to harmonic maps.
ISSN:2331-8422