Geodesic
Specialized Orthonormal Frames and Embedding
Symmetry, integrability and geometry: methods and applications, Tome 9 (2013)

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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 pseudo-Riemannian geometries. The specializations are closed sets of linear constraints on the connection 1-forms of the framing. The embeddings can be isometric, as in minimal surfaces or Regge–Teitelboim gravity, or torsion-free, as in Einstein vacuum gravity. Involutive exterior differential systems are given, and their Cartan character tables calculated to express the well-posedness of the underlying partial differential embedding and specialization equations.
Keywords: embedding; orthonormal frames; Cartan theory. 
Frank B. Estabrook. Specialized Orthonormal Frames and Embedding. Symmetry, integrability and geometry: methods and applications, Tome 9 (2013). http://geodesic.mathdoc.fr/item/SIGMA_2013_9_a11/
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