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Geodesic Flow on the Normal Congruence of a Minimal Surface

  • Brendan Guilfoyle
  • Wilhelm Klingenberg
Chapter
Part of the Progress in Mathematics book series (PM, volume 265)

Abstract

We study the geodesic flow on the normal line congruence of a minimal surface in ℝ3 induced by the neutral Kähler metric on the space of oriented lines. The metric is lorentz with isolated degenerate points and the flow is shown to be completely integrable. In addition, we give a new holomorphic description of minimal surfaces in ℝ3 and relate it to the classical Weierstrass representation.

Keywords

Geodesic flow minimal surface oriented lines 

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2007

Authors and Affiliations

  • Brendan Guilfoyle
    • 1
  • Wilhelm Klingenberg
    • 2
  1. 1.Department of Computing and MathematicsInstitute of Technology, Tralee Clash TraleeCo. KerryIreland
  2. 2.Department of Mathematical SciencesUniversity of DurhamDurhamUK

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