Geodesic Flow on Global Holomorphic Sections of TS2

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

0000-0002-7437-5046

Document Type

Article

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Disciplines

Mathematics | Physical Sciences and Mathematics

Publication Details

Bulletin of the Belgian Mathematical Socity, vol. 14(2). Copyright © 2007 The Belgian Mathematical Society

Abstract

We study the geodesic flow on the global holomorphic sections of the bundle π : TS2 → S 2 induced by the neutral K¨ahler metric on the space of oriented lines of R 3 , which we identify with TS2 . This flow is shown to be completely integrable when the sections are symplectic, and the behaviour of the geodesics is described.

Recommended Citation

Brendan Guilfoyle. Wilhelm Klingenberg. "Geodesic Flow on Global Holomorphic Sections of TS2." Bull. Belg. Math. Soc. Simon Stevin 14 (2) 363 - 371, June 2007. https://doi.org/10.36045/bbms/1179839229