Resumo

SALVAI, Marcos. Geodesics of the space of oriented lines of euclidean space. Rev. Unión Mat. Argent. [online]. 2006, vol.47, n.2, pp.109-114. ISSN 0041-6932.

For or let be the space of oriented lines in . In a previous article we characterized up to equivalence the metrics on which are invariant by the induced transitive action of a connected closed subgroup of the group of Euclidean motions (they exist only in such dimensions and are pseudo-Riemannian of split type) and described explicitly their geodesics. In this short note we present the geometric meaning of the latter being null, time- or space-like. On the other hand, it is well-known that is diffeomorphic to , the space of all oriented geodesics of the -dimensional hyperbolic space. For and , we compute now a pseudo-Riemannian invariant of (involving its periodic geodesics) that will be useful to show that and are not isometrically equivalent, provided that the latter is endowed with any of the metrics which are invariant by the canonical action of the identity component of the isometry group of .

Palavras-chave : oriented lines; minitwistor; pseudo-Riemannian; quaternions; octonions; pitch.

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