Generalized Riemann minimal surfaces examples in three-dimensional manifolds products

L. Hauswirth

Generalized Riemann minimal surfaces examples in three-dimensional manifolds products

Differential Geometry 2007-05-23 v1 Classical Analysis and ODEs

Authors: L. Hauswirth

Abstract

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.

Keywords

minimal surfaces surfaces with constant mean curvature surface theory

Cite

@article{arxiv.math/0507187,
  title  = {Generalized Riemann minimal surfaces examples in three-dimensional manifolds products},
  author = {L. Hauswirth},
  journal= {arXiv preprint arXiv:math/0507187},
  year   = {2007}
}

Comments

23 pages, 8 figures

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