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Null hypersurfaces in Lorentzian manifolds: I

Published online by Cambridge University Press:  24 October 2008

K. Katsuno
K. Katsuno
Affiliation:
Queen Elizabeth College, London
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Extract

This paper is concerned with geometrical properties of null hypersurfaces in Lorentzian manifolds. Null hypersurfaces have metrics with vanishing determinants and this degeneracy of these metrics leads to several difficulties. First, the contravariant metric cannot immediately be defined, so the connection cannot be specified uniquely in the normal way. Secondly, the normal is a null vector lying in the tangent plane, which makes it necessary to look for some other vector to rig the hypersurface, and makes it impossible to normalise the normal in the usual way. These problems are considered in this paper.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 88 , Issue 1 , July 1980 , pp. 175 - 182
Copyright
Copyright © Cambridge Philosophical Society 1980

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References

REFERENCES

(1)Bonnor, W. B.Null hypersurfaces in Minkowski space–time. Tensor (N.S.) 24 (1972), 329–345.Google Scholar
(2)Dautcourt, G.Characteristic hypersurfaces in general relativity I. J. Math. Phys. 8 (1967), 1492–1501.CrossRefGoogle Scholar
(3)Kammerer, J. B.Théorème de Peering et hypersurfaces isotropes, Rend. Circ. Mat. Palermo (série II) 16 (1967) 129–202.CrossRefGoogle Scholar
(4)Lemmer, G.On covariant differentiation within a null hypersurface. Nuovo Cimento 37 (1965), 1659–1672.CrossRefGoogle Scholar
(5)Rosca, R.Sur les hypersurfaces isotropes de défaut 1 incluses dans une variété lorent-zienne, C. R. Acad. Sci. Paris 292 (1971) 393–396.Google Scholar
(6)Rosca, R.On null hypersurfaces of a Lorentzian manifold, Tensor (N.S.) 23 (1972), 66–74.Google Scholar
(7)Cagnac, F.Géométrie des hypersurfaces isotropes, C.R. Acad. Sci. Paris, 261 (1965), 3045–3048.Google Scholar
(8)Dautcourt, G.Zur Differential geometrie singulärer Riemannscher Räume, Math. Nachr. 36 (1968), 311–322.CrossRefGoogle Scholar
(9)Galstyan, N. G.The rigging of isotropic hypersurfaces, Dokl. Akad. Nauk. Arm. SSR, 45 (1967), 97–100.Google Scholar
(10)Rosca, R. and Vanhecke, L. Les sous-variétés isotropes et pseudo-isotropes d'une variété hyperbolique à n dimensions. (Verhand. von de Kon. Acad. voor Wetens Chap., Lett, en Scho. Kun. van Belg. (Klasse der Weter.) Jaargang xxxviii, Nr 136, 1976).Google Scholar
(11)Sokolowski, L. M.The Gauss-Codazzi equations and field equations for a spherical case of null hypersurfaces in the theory of gravitation. Acta Phys. Polon. 4 (1975), B6.Google Scholar
(12)Willmore, T. J.An introduction to differential geometry (Oxford, 1959), 237–238. pp.Google Scholar