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Geodesic Flow on Global Holomorphic Sections of TS^2

Brendan Guilfoyle·Wilhelm Klingenberg
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Abstract

We study the geodesic flow on the global holomorphic sections of the bundle $\pi:{TS}^2\to {S}^2$ induced by the neutral K\"ahler metric on the space of oriented lines of ${\Bbb{R}}^3$, which we identify with ${TS}^2$. This flow is shown to be completely integrable when the sections are symplectic and the behaviour of the geodesics is described.

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Brendan Guilfoyle, Wilhelm Klingenberg. 2006-02-23. Geodesic Flow on Global Holomorphic Sections of TS^2. https://doi.org/10.36045/bbms%2F1179839229

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