Communications in Mathematical Physics

, Volume 40, Issue 3, pp 273–282 | Cite as

Conformal groups and conformally equivalent isometry groups

  • L. Defrise-Carter


It is shown that if ann dimensional Riemannian or pseudo-Riemannian manifold admits a proper conformal scalar, every (local) conformal group is conformally isometric, and that if it admits a proper conformal gradient every (local) conformal group is conformally homothetic. In the Riemannian case there is always a conformal scalar unless the metric is conformally Euclidean. In the case of a Lorentzian 4-manifold it is proved that the only metrics with no conformal scalars (and hence the only ones admitting a (local) conformal group not conformally isometric) are either conformal to the plane wave metric with parallel rays or conformally Minkowskian.


Neural Network Manifold Statistical Physic Complex System Nonlinear Dynamics 
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Copyright information

© Springer-Verlag 1975

Authors and Affiliations

  • L. Defrise-Carter
    • 1
  1. 1.Girton CollegeCambridgeEngland

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