Geodesic Flow on Global Holomorphic Sections of TS^2

Abstract

We study the geodesic flow on the global holomorphic sections of the bundle $\pi :{TS}^2\to S^2$ induced by the neutral Kähler metric on the space of oriented lines of ${\mathbb{R}}^3$, 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.

AMS-LATEX 7 pages, 2 figures

Cited by in corpus (1)

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