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ON THE GEOMETRY OF THE SPACE OF ORIENTED LINES OF THE HYPERBOLIC SPACE

Published online by Cambridge University Press:  09 August 2007

MARCOS SALVAI
MARCOS SALVAI*
Affiliation:
FAMAF – CIEM, Ciudad Universitaria, 5000 Córdoba, Argentina e-mail: salvai@mate.uncor.edu
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Abstract

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Let H be the n-dimensional hyperbolic space of constant sectional curvature –1 and let G be the identity component of the isometry group of H. We find all the G-invariant pseudo-Riemannian metrics on the space of oriented geodesics of H (modulo orientation preserving reparametrizations). We characterize the null, time- and space-like curves, providing a relationship between the geometries of and H. Moreover, we show that is Kähler and find an orthogonal almost complex structure on .

Keywords

53A5553C2253C3553C5053D25
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 49 , Issue 2 , May 2007 , pp. 357 - 366
Copyright
Copyright © Glasgow Mathematical Journal Trust 2007

References

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