Pacific Journal of Mathematics

Nonuniqueness of the metric in Lorentzian manifolds.

G. K. Martin and G. Thompson

Article information

Source
Pacific J. Math., Volume 158, Number 1 (1993), 177-187.

Dates
First available in Project Euclid: 8 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1102634615

Mathematical Reviews number (MathSciNet)
MR1200834

Zentralblatt MATH identifier
0799.53032

Subjects
Primary: 53C50: Lorentz manifolds, manifolds with indefinite metrics

Citation

Martin, G. K.; Thompson, G. Nonuniqueness of the metric in Lorentzian manifolds. Pacific J. Math. 158 (1993), no. 1, 177--187. https://projecteuclid.org/euclid.pjm/1102634615


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References

  • [I] G.S.Hall and C.B.G.Mclntosh, Algebraic determination of the metric from the curvature in general relativity, Internat. J. Theoret. Phys. 22 (1983), 469.
  • [2] G. S.Hall, Curvature collineations andthedetermination of the metricfrom the curvature ingeneral relativity, Gen.Relativity Gravitation, 15(1983), 581.
  • [3] G. S.Hall, Connections andsymmetries in spacetime, Gen.Relativity Gravitation, 20 (1988), 399.
  • [4] G. S.Hall, Covariantly constant tensors andholonomy structure ingeneral relativity, J. Math. Phys., 32 (1), (1991), 181-187.
  • [5] E.Ihrig, An exact determination of the gravitational potentials gij in terms of the gravitation fields R\jk ,J. Math. Phys., 16 (1975),54-55.
  • [6] M. Kossowski and G. Thompson, Submersive second order ordinary differential equations, Math. Proc. CambridgePhilos. Soc, 110(1991),207-224.
  • [7] J. Schell,Classification offour-dimensional Riemannian spaces,J.Math. Phys., 2 (1961), 202.
  • [8] F.Uhlig, The number of vectorsjointly annihilated by tworeal quadratic forms determines theinertia of matrices in theassociated pencil, Pacific J. Math., 49 (1973), 537-542.
  • [9] F.Uhlig, A canonicalform for a pair of real symmetric matrices that generate a nonsingular pencil, Linear Algebra Appl., 14 (1976), 189-209.
  • [10] A. G.Walker, Canonical form for a Riemannian space with a parallel field of null planes, Quart. J. Math. Oxford, (2), 1 (1950),69-79.
  • [II] K. Weierstrass, Zur theorie der bilinearen undquadratischen Formen, Monat- sber. Akad-Wiss. BerL, (1868), 310.
  • [12] T. J. Willmore, An Introduction to Differential Geometry, Oxford University Press, (1959).
  • [13] H. Wu, On the de Rham decomposition theorem, Illinois J. Math., 8 (1964), 291-311.
  • [14] H. Wu, Holonomy groups in indefinite metrics, Pacific J. Math., 20 (1967), 351- 392.