Isometry Groups with Surface-Orthogonal Trajectories
Open Access
- 1 September 1967
- journal article
- Published by Walter de Gruyter GmbH in Zeitschrift für Naturforschung A
- Vol. 22 (9) , 1351-1355
- https://doi.org/10.1515/zna-1967-0911
Abstract
It is shown that the trajectories of an isometry group admit orthogonal surfaces if the sub-group of stability leaves no vector in the tangent space of the trajectories fixed. A necessary and sufficient condition is given that the trajectories of an Abelian group admit orthogonal surfaces. In spacetimes which admit an Abelian G2 of isometries, the trajectories admit orthogonal 2-surfaces if a timelike congruence exists with the following properties: the curves lie in the trajectories and are invariant under G2; ωα and üα are linearly independent and orthogonal to the trajectories.Keywords
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