Specialized Orthonormal Frames and Embedding
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-form...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2013 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2013
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/149215 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Specialized Orthonormal Frames and Embedding / F.B. Estabrook // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 6 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862705901537853440 |
|---|---|
| author | Estabrook, F.B. |
| author_facet | Estabrook, F.B. |
| citation_txt | Specialized Orthonormal Frames and Embedding / F.B. Estabrook // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 6 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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.
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| first_indexed | 2025-12-07T16:56:25Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-149215 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T16:56:25Z |
| publishDate | 2013 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Estabrook, F.B. 2019-02-19T18:48:06Z 2019-02-19T18:48:06Z 2013 Specialized Orthonormal Frames and Embedding / F.B. Estabrook // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 6 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 83C20; 57R40; 58A15 DOI: http://dx.doi.org/10.3842/SIGMA.2013.012 https://nasplib.isofts.kiev.ua/handle/123456789/149215 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. This paper is a contribution to the Special Issue “Symmetries of Dif ferential Equations: Frames, Invariants and Applications”. The full collection is available at http://www.emis.de/journals/SIGMA/SDE2012.html.
 I thank the JPL Of fice of the Chief Scientist for a visiting appointment during which this research was carried out, and the Science Division for hospitality. My
 colleagues John W. Armstrong, Curt Cutler, Massimo Tinto and Michele Vallisneri gave constant stimulus and support. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Specialized Orthonormal Frames and Embedding Article published earlier |
| spellingShingle | Specialized Orthonormal Frames and Embedding Estabrook, F.B. |
| title | Specialized Orthonormal Frames and Embedding |
| title_full | Specialized Orthonormal Frames and Embedding |
| title_fullStr | Specialized Orthonormal Frames and Embedding |
| title_full_unstemmed | Specialized Orthonormal Frames and Embedding |
| title_short | Specialized Orthonormal Frames and Embedding |
| title_sort | specialized orthonormal frames and embedding |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/149215 |
| work_keys_str_mv | AT estabrookfb specializedorthonormalframesandembedding |