Geodesic Flow on Global Holomorphic Sections of TS^2

Details Geodesic Flow on Global Holomorphic Sections of TS^2 Geodesic Flow on Global Holomorphic Sections of TS^2

2006-02-23

arxiv.org/abs/math/0602512v1

Bull. Belg. Math. Soc. 13 (2006) 1-9.

Mathematics

Differential Geometry

AMS-LATEX 7 pages, 2 figures

Scientific paper

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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