Communications in Mathematical Physics

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

Lorentzian 4 dimensional manifolds with “local isotropy”

  • M. Cahen
  • L. Defrise


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.


Neural Network Manifold Statistical Physic Complex System Nonlinear Dynamics 
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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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