Tractor bundle

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In conformal geometry, the tractor bundle is a particular vector bundle constructed on a conformal manifold whose fibres form an effective representation of the conformal group (see associated bundle).

The term tractor is a portmanteau of "Tracy Thomas" and "twistor", the bundle having been introduced first by T. Y. Thomas as an alternative formulation of the Cartan conformal connection,[1] and later rediscovered within the formalism of local twistors and generalized to projective connections by Michael Eastwood et al. in [2]


  1. ^ Thomas, T. Y., "On conformal differential geometry", Proc. N.A.S. 12 (1926), 352–359; "Conformal tensors", Proc. N.A.S. 18 (1931), 103–189.
  2. ^ Bailey, T. N.; Eastwood, M. G.; Gover, A. R., "Thomas's structure bundle for conformal, projective and related structures", Rocky Mountain J. 24 (1994), 1191–1217.