
SIGMA 9 (2013), 012, 5 pages arXiv:1206.5229
https://doi.org/10.3842/SIGMA.2013.012
Contribution to the Special Issue “Symmetries of Differential Equations: Frames, Invariants and Applications”
Specialized Orthonormal Frames and Embedding
Frank B. Estabrook
Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109 USA
Received October 09, 2012, in final form February 12, 2013; Published online February 15, 2013
Abstract
We discuss some specializations of the frames of flat orthonormal frame bundles over
geometries of indefinite signature, and the resulting symmetries of families of embedded
Riemannian or pseudoRiemannian geometries.
The specializations are closed sets of linear constraints on the connection 1forms of the framing.
The embeddings can be isometric, as in minimal surfaces or ReggeTeitelboim gravity, or
torsionfree, as in Einstein vacuum gravity.
Involutive exterior differential systems are given, and their Cartan character tables
calculated to express the wellposedness of the underlying partial differential embedding
and specialization equations.
Key words:
embedding; orthonormal frames; Cartan theory.
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