NASA Logo

NTRS

NTRS - NASA Technical Reports Server

Back to Results
Covariance and the hierarchy of frame bundlesThis is an essay on the general concept of covariance, and its connection with the structure of the nested set of higher frame bundles over a differentiable manifold. Examples of covariant geometric objects include not only linear tensor fields, densities and forms, but affinity fields, sectors and sector forms, higher order frame fields, etc., often having nonlinear transformation rules and Lie derivatives. The intrinsic, or invariant, sets of forms that arise on frame bundles satisfy the graded Cartan-Maurer structure equations of an infinite Lie algebra. Reduction of these gives invariant structure equations for Lie pseudogroups, and for G-structures of various orders. Some new results are introduced for prolongation of structure equations, and for treatment of Riemannian geometry with higher-order moving frames. The use of invariant form equations for nonlinear field physics is implicitly advocated.
Document ID
19880039048
Acquisition Source
Legacy CDMS
Document Type
Reprint (Version printed in journal)
External Source(s)
Authors
Estabrook, Frank B.
(California Institute of Technology Jet Propulsion Laboratory, Pasadena, United States)
Date Acquired
August 13, 2013
Publication Date
January 1, 1987
Publication Information
Publication: Acta Applicandae Mathematicae
Volume: 8
ISSN: 0167-8019
Subject Category
Theoretical Mathematics
Accession Number
88A26275
Distribution Limits
Public
Copyright
Other

Available Downloads

There are no available downloads for this record.
No Preview Available