Geodesic
ON THE GEOMETRY OF THE SPACE OF ORIENTED LINES OF THE HYPERBOLIC SPACE
Glasgow mathematical journal, Tome 49 (2007) no. 2, pp. 357-366

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DOI

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 .
DOI : 10.1017/S0017089507003710
Mots-clés : 53A55, 53C22, 53C35, 53C50, 53D25 
SALVAI, MARCOS. ON THE GEOMETRY OF THE SPACE OF ORIENTED LINES OF THE HYPERBOLIC SPACE. Glasgow mathematical journal, Tome 49 (2007) no. 2, pp. 357-366. doi: 10.1017/S0017089507003710
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     title = {ON {THE} {GEOMETRY} {OF} {THE} {SPACE} {OF} {ORIENTED} {LINES} {OF} {THE} {HYPERBOLIC} {SPACE}},
     journal = {Glasgow mathematical journal},
     pages = {357--366},
     year = {2007},
     volume = {49},
     number = {2},
     doi = {10.1017/S0017089507003710},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089507003710/}
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