H-Space with a Cosmological Constant

Details H-Space with a Cosmological Constant H-Space with a Cosmological Constant

Mar 1982

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1982rspsa.380..171l&link_type=abstract

Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, Volume 380, Issue 1778, pp. 171-185

Mathematics

Logic

26

Scientific paper

It is demonstrated that a real-analytic 3-manifold with Riemannian conformal metric is naturally the conformal infinity of a germ-unique real-analytic 4-manifold with real-analytic Riemannian metric satisfying the self-dual Einstein equations with cosmological constant - 1. Moreover, this result holds if 'Riemannian' is replaced in the first case by 'Lorentzian' (i.e. signature + - -) and in the second case by 'pseudo-Riemannian with signature + + - -', or if 'real-analytic' is replaced by 'complex-analytic' and 'Riemannian' is replaced by 'holomorphic'. This provides a cosmological-constant analogue of Newman's H-space construction (Newman 1976, 1977).

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