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Moving frames and prolongation algebrasDifferential ideals generated by sets of 2-forms which can be written with constant coefficients in a canonical basis of 1-forms are considered. By setting up a Cartan-Ehresmann connection, in a fiber bundle over a base space in which the 2-forms live, one finds an incomplete Lie algebra of vector fields in the fields in the fibers. Conversely, given this algebra (a prolongation algebra), one can derive the differential ideal. The two constructs are thus dual, and analysis of either derives properties of both. Such systems arise in the classical differential geometry of moving frames. Examples of this are discussed, together with examples arising more recently: the Korteweg-de Vries and Harrison-Ernst systems.
Document ID
19830039825
Acquisition Source
Legacy CDMS
Document Type
Reprint (Version printed in journal)
External Source(s)
Authors
Estabrook, F. B.
(California Institute of Technology, Jet Propulsion Laboratory, Pasadena CA, United States)
Date Acquired
August 11, 2013
Publication Date
November 1, 1982
Publication Information
Publication: Journal of Mathematical Physics
Volume: 23
Subject Category
Theoretical Mathematics
Accession Number
83A21043
Funding Number(s)
CONTRACT_GRANT: NAS7-100
Distribution Limits
Public
Copyright
Other

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