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Lorentzian 4 dimensional manifolds with “local isotropy”

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Abstract

We define “locally isotropic” spaces, as spaces in which there exists, in the tangent space at each pointP, a subgroupA (P) (of dimension at least 1) of the Lorentz groupL ↑+ , leaving the Riemann tensor and its 2 first covariant derivatives invariant; the subgroupsA(P) are assumed to be conjugate inL ↑+ . These spaces admit a group of local isometriesG. IfI P denotes the subgroup ofG leavingP fixed, thendA (P)=I P . All spaces of petrov type D, admitting local isotropy are determined.

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Authors and Affiliations

  1. Université libre de Bruxelles, Belgium

    M. Cahen & L. Defrise

  2. Department of Mathematics, University of California, Berkeley Campus, Berkeley, California, USA

    M. Cahen

Authors
  1. M. Cahen
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  2. L. Defrise
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On leave of absence of the Southwest Center for Advanced Studies Dallas.

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Cahen, M., Defrise, L. Lorentzian 4 dimensional manifolds with “local isotropy”. Commun.Math. Phys. 11, 56–76 (1968). https://doi.org/10.1007/BF01654301

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  • DOI: https://doi.org/10.1007/BF01654301

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