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Communications in Mathematical Physics

, Volume 11, Issue 1, pp 56–76 | Cite as

Lorentzian 4 dimensional manifolds with “local isotropy”

  • M. Cahen
  • L. Defrise
Article

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.

Keywords

Neural Network Manifold Statistical Physic Complex System Nonlinear Dynamics 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1968

Authors and Affiliations

  • M. Cahen
    • 1
    • 2
  • L. Defrise
    • 1
  1. 1.Université libre de BruxellesBelgium
  2. 2.Department of MathematicsUniversity of CaliforniaBerkeleyUSA

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