Geodesic Flow on the Normal Congruence of a Minimal Surface

Authors

• BRENDAN GUILFOYLE, School of Science, Technology, Engineering and Mathematics, Institute of Technology, Tralee, Clash, Tralee, Co. Kerry, Ireland.Follow
• Wilhelm Klingenberg, Department of Mathematical Sciences, University of Durham, Durham, DH1 3LE, UK

ORCID

https://orcid.org/ 0000-0002-7437-5046

Document Type

Book Part

Disciplines

Mathematics | Physical Sciences and Mathematics

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.

Recommended Citation

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