Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Tractor calculi for parabolic geometries
HTML articles powered by AMS MathViewer

by Andreas Čap and A. Rod Gover PDF
Trans. Amer. Math. Soc. 354 (2002), 1511-1548 Request permission

Abstract:

Parabolic geometries may be considered as curved analogues of the homogeneous spaces $G/P$ where $G$ is a semisimple Lie group and $P\subset G$ a parabolic subgroup. Conformal geometries and CR geometries are examples of such structures. We present a uniform description of a calculus, called tractor calculus, based on natural bundles with canonical linear connections for all parabolic geometries. It is shown that from these bundles and connections one can recover the Cartan bundle and the Cartan connection. In particular we characterize the normal Cartan connection from this induced bundle/connection perspective. We construct explicitly a family of fundamental first order differential operators, which are analogous to a covariant derivative, iterable and defined on all natural vector bundles on parabolic geometries. For an important subclass of parabolic geometries we explicitly and directly construct the tractor bundles, their canonical linear connections and the machinery for explicitly calculating via the tractor calculus.
References
Similar Articles
Additional Information
  • Andreas Čap
  • Affiliation: Institut für Mathematik, Universität Wien, Strudlhofgasse 4, A–1090 Wien, Austria and International Erwin Schrödinger Institute for Mathematical Physics, Boltzmanngasse 9, A–1090 Wien, Austria
  • Email: Andreas.Cap@esi.ac.at
  • A. Rod Gover
  • Affiliation: Department of Mathematics, The University of Auckland, Private Bag 92019, Auckland, New Zealand
  • MR Author ID: 335695
  • Email: gover@math.auckland.ac.nz
  • Received by editor(s): July 17, 2000
  • Published electronically: November 20, 2001
  • © Copyright 2001 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 354 (2002), 1511-1548
  • MSC (2000): Primary 53B15, 53C05, 53C07, 53C15; Secondary 32V05, 53A20, 53A30, 53A40, 53A55
  • DOI: https://doi.org/10.1090/S0002-9947-01-02909-9
  • MathSciNet review: 1873017