Geodesic Flow on Global Holomorphic Sections of TS^2

Klingenberg, Wilhelm; Guilfoyle, Brendan

Abstract

We study the geodesic flow on the global holomorphic sections of the bundle π:TS2→S2π:TS2→S2 induced by the neutral Kähler metric on the space of oriented lines of R3R3, which we identify with TS2TS2. This flow is shown to be completely integrable when the sections are symplectic, and the behaviour of the geodesics is described.

Citation

Klingenberg, W., & Guilfoyle, B. (2007). Geodesic Flow on Global Holomorphic Sections of TS^2. Bulletin of the Belgian Mathematical Society Simon Stevin (Printed), 14(2), 363-371

• Journal Article Type: Article
• Publication Date: 2007-06
• Journal: Bulletin of the Belgian Mathematical Society, Simon Stevin.
• Print ISSN: 1370-1444
• Electronic ISSN: 2034-1970
• Publisher: The Belgian Mathematical Society
• Volume: 14
• Issue: 2
• Pages: 363-371
• Public URL: https://durham-repository.worktribe.com/output/1579290
• Publisher URL: http://projecteuclid.org/euclid.bbms/1179839229