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Lorentzian 4 dimensional manifolds with "local isotropy"

par Cahen, Michel ;Defrise, Lucette
Référence Communications in Mathematical Physics, 11, 1, page (56-76)
Publication Publié, 1968-03

Article révisé par les pairs

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Résumé :

We define "locally isotropic" spaces, as spaces in which there exists, in the tangent space at each point P, a subgroup A (P) (of dimension at least 1) of the Lorentz group L+↑, leaving the Riemann tensor and its 2 first covariant derivatives invariant; the subgroups A(P) are assumed to be conjugate in L+↑. These spaces admit a group of local isometries G. If IP denotes the subgroup of G leaving P fixed, then dA (P)=IP. All spaces of petrov type D, admitting local isotropy are determined. © 1968 Springer-Verlag.