Thomas’s structure bundle for conformal, projective and related structures. (English) Zbl 0828.53012

Bailey, T. N.; Eastwood, M. G.; Gover, R. A.

Rocky Mt. J. Math. 24, No. 4, 1191-1217 (1994).

In this paper the authors present the construction of the tractor bundle with the tractor connection of a conformal manifold. This construction goes back to T. Y. Thomas [Proc. Natl. Acad. Sci. 11, 588-589 (1925)]. Conformal flatness is equivalent to the flatness of the tractor connection. Then one can discuss conformally invariant differential operators on the tractor bundle. The tractor bundle is an associated vector bundle to a principal bundle. Under this correspondence one gets a relation between the tractor connection and the Cartan connection on the principal bundle. Similar constructions are also possible for other geometric structures, of which the authors discuss projective and paraconformal structures.

Reviewer: H.-B.Rademacher (Leipzig)

MSC:

53A30	Conformal differential geometry (MSC2010)
53A20	Projective differential geometry

Keywords:

tractor bundle; tractor connection; conformal manifold; Cartan connection

References:

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