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The Geometry Of The Space Of Oriented Geodesics Of Hyperbolic 3-Space, Nikos Georgiou
The Geometry Of The Space Of Oriented Geodesics Of Hyperbolic 3-Space, Nikos Georgiou
Theses
In this thesis we construct a Kähler structure (J, Ω, G) on the space L(H3) of oriented geodesics of hyperbolic 3-space H3 and investigate its properties. We prove that (L(H3),J) is biholomorphic to (see thesis pdf), and that the Kähler metric G is of neutral signature, conformally flat and scalar flat.
We establish that the identity component of the isometry group of the metric G on L(H3) is isomorphic to the identity component of the hyperbolic isometry group. We show that the geodesics of G correspond to ruled minimal surfaces in H3, which …