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Null hypersurfaces in Lorentzian manifolds II

Published online by Cambridge University Press:  24 October 2008

K. Katsuno
Affiliation:
Queen Elizabeth College, London

Extract

This paper is a continuation of (8), and is concerned with geometrical properties of special null hypersurfaces. In particular, on a one-parameter family of null hypersurfaces in four-dimensional Lorentzian manifold V4, we consider the relation between their normal and the Debever vectors, especially repeated ones. Throughout this paper, the same notations as those in (8) are used.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1981

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References

REFERENCES

(1)Bonnor, W. B.Null hypersurfaces in Minkowski space-time. Tensor (N.S.) 24 (1072), 329345.Google Scholar
(2)Cahen, M., Debever, R. and Defrise, L.A complex vectorial formalism in general relativity. J. Math. Mech. 16 (1967), 761785.Google Scholar
(3)Dautcourt, G.Characteristic hypersurfaces in general relativity. I.J. of Math. Phys. 8 (1967), 14921501.Google Scholar
(4)Eisenhart, L. P.Riemannian Geometry (Princeton, 1949).Google Scholar
(5)Hall, G. S.Riemannian curvature and the Petrov classification. Z. Naturforsch. 33a (1978), 559562.Google Scholar
(6)Israel, W.Differential forms in General Relativity (Comm. Dublin Inst. Adv. Stud. series A, no. 19).Google Scholar
(7)Kammerer, J. B.Théorème de Peeling et hypersurfaces isotropes. Rend. Circ. Mat. di Palermo, Serie II, 16 (1967), 129202.CrossRefGoogle Scholar
(8)Katsuno, K.Null hypersurfaces in Lorentzian manifold I. Math. Proc. Cambridge Philos. Soc. 88 (1980), 175182.Google Scholar
(9)Katsuno, K. Null hypersurfaces in Minkowski space-time. (To appear.)Google Scholar
(10)Lemmer, G.On covariant differentiation within a null hypersurface. Nuovo Cimento, 37 (1965), 16591672.Google Scholar
(11)Rosca, R.On null hypersurfaces of a Lorentzian manifold. Tensor N.S. 23 (1972), 6674.Google Scholar
(12)Rosca, R.Sur les hypersurfaces isotropes de défaut 1 incluses dans une variété lorentzienne. C.R. Acad. Sci. Paris 272 (1971), 393396.Google Scholar
(13)Synge, J. L.Relativity, the general theory (North Holland Publishing Company, Amsterdam, 1964).Google Scholar
(14)Willmore, T. J.An introduction to differential geometry, p. 237238. (Oxford, 1964).Google Scholar