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.
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Dedicated to the memory of Sasha Reznikov
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© 2007 Birkhäuser Verlag Basel/Switzerland
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Guilfoyle, B., Klingenberg, W. (2007). Geodesic Flow on the Normal Congruence of a Minimal Surface. In: Kapranov, M., Manin, Y.I., Moree, P., Kolyada, S., Potyagailo, L. (eds) Geometry and Dynamics of Groups and Spaces. Progress in Mathematics, vol 265. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8608-5_11
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DOI: https://doi.org/10.1007/978-3-7643-8608-5_11
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-7643-8607-8
Online ISBN: 978-3-7643-8608-5
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