SPACE–TIMES WITH A TWO-DIMENSIONAL GROUP OF CONFORMAL MOTIONS
1996 ◽
Vol 11
(05)
◽
pp. 845-861
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Keyword(s):
The necessary and sufficient conditions for a space–time to admit a two-dimensional group of conformal motions (and, in particular, of homothetic motions) acting on nonnull orbits are found in the compacted spin-coefficient formalism. Although the discussion is restricted to the case of spacelike orbits, similar results are readily obtained for timelike orbits via the (modified) Sachs star operation. A number of theorems are obtained dealing with such topics as the Gaussian curvature of the group orbits, orthogonal transitivity, and hypersurface orthogonality of the conformal Killing vectors. A simple proof is presented of a generalization of a theorem due to Papapetrou.
1981 ◽
Vol 4
(3)
◽
pp. 473-484
2001 ◽
Vol 32
(3)
◽
pp. 201-209
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1972 ◽
Vol 18
(2)
◽
pp. 129-136
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1999 ◽
Vol 129
(5)
◽
pp. 1081-1105
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2002 ◽
Vol 12
(12)
◽
pp. 2957-2966
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1992 ◽
Vol 439
(1905)
◽
pp. 103-113
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2005 ◽
Vol 135
(5)
◽
pp. 985-998
◽