Thomas's structure bundle for conformal, projective and related structures
type: Item
instance of: scholarly article
title: Thomas's structure bundle for conformal, projective and related structures
zbMATH Open document ID: 0828.53012
author: M. Eastwood
author: Rod Gover
author: Toby Bailey
published in: Rocky Mountain Journal of Mathematics
publication date: 1995-07-05T00:00:00Z
review text: 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 \textit{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.
Mathematics Subject Classification ID: 53A30
Mathematics Subject Classification ID: 53A20
zbMATH DE Number: 757768
zbMATH Keywords: tractor bundle
zbMATH Keywords: tractor connection
zbMATH Keywords: conformal manifold
zbMATH Keywords: Cartan connection
reviewed by: Hans-Bert Rademacher
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1216/rmjm/1181072333
OpenAlex ID: W1986614997
cites work: Complex Paraconformal Manifolds – their Differential Geometry and Twistor Theory
cites work: Conformal Circles and Parametrizations of Curves in Conformal Manifolds
cites work: Invariant theory for conformal and CR geometry
cites work: Exceptional Invariants in the Parabolic Invariant Theory of Conformal Geometry
cites work: Almost Hermitian symmetric manifolds. I: Local twistor theory
cites work: Conformally Invariant Operators: Singular Cases
cites work: A duality theorem for Willmore surfaces
cites work: Conformally invariant differential operators on Minkowski space and their curved analogues
cites work: A conformally invariant Maxwell gauge.
cites work: Q3738176
cites work: CONFORMALLY INVARIANT OPERATORS OF STANDARD TYPE
cites work: Conformally Invariant Powers of the Laplacian, I: Existence
cites work: Q3656899
cites work: Q4195061
cites work: Q5658761
cites work: Q3324593
cites work: Q3719405
cites work: Quaternionic Kaehler manifolds
cites work: Differential geometry of quaternionic manifolds
cites work: Conformal Tensors. (First Note.)
cites work: Q4756474
cites work: Q3229050
DOI: 10.1216/RMJM/1181072333
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description: scientific article; zbMATH DE number 757768