Curvature structure in general relativity
- 1 February 1988
- journal article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 29 (2) , 420-427
- https://doi.org/10.1063/1.528030
Abstract
This paper investigates the extent to which the curvature structure of space-time determines the metric stucture. It continues the work of earlier papers by prescribing the curvature structure and the curvature covariant derivatives up to certain orders. It is shown that, with the exception of the so-called generalized pp waves, the curvature and its first and second covariant derivatives essentially determine the metric up to coordinate transformations.Keywords
This publication has 12 references indexed in Scilit:
- Curvature collineations and the determination of the metric from the curvature in general relativityGeneral Relativity and Gravitation, 1983
- Algebraic determination of the metric from the curvature in general relativityInternational Journal of Theoretical Physics, 1983
- Spacetimes admitting a vector field whose inner product with the Riemann tensor is zeroJournal of Mathematical Physics, 1982
- Recurrence conditions in space-timeJournal of Physics A: General Physics, 1977
- The classification of the Ricci tensor in general relativity theoryJournal of Physics A: General Physics, 1976
- Complex recurrent space-timesProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1972
- Strongly curvature-preserving transformations of pseudo-Riemmanian manifoldsTohoku Mathematical Journal, 1967
- Flat-space metric in general relativity theoryAnnals of Physics, 1963
- ON SYMMETRIC RECURRENT TENSORS OF THE SECOND ORDERThe Quarterly Journal of Mathematics, 1951
- ON PARALLEL FIELDS OF PARTIALLY NULL VECTOR SPACESThe Quarterly Journal of Mathematics, 1949