Geodesic flow on global holomorphic sections of \({TS}^2\) (Q2381150)

The authors consider a natural isometry invariant Kähler metric on the space of all oriented lines in the Euclidean three-space. This moduli space is isomorphic to the tangent bundle of the two-sphere where the projection corresponds to a line in its direction, the Kähler metric is indefinite and has a neutral signature. The authors consider the restriction of the Kähler metric to a global holomorphic section of the tangent bundle, prove that the geodesic flow on the induced metric is integrable and describe the behaviour of geodesics.