Lie Algebroid Invariants for Subgeometry
We investigate the infinitesimal invariants of an immersed submanifold Σ of a Klein geometry M ≅ G/H, and in particular an invariant filtration of Lie algebroids over Σ. The invariants are derived from the logarithmic derivative of the immersion of Σ into M, a complete invariant introduced in the co...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2018 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2018
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/209788 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Lie Algebroid Invariants for Subgeometry / A.D. Blaom // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 21 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862670246899351552 |
|---|---|
| author | Blaom, A.D. |
| author_facet | Blaom, A.D. |
| citation_txt | Lie Algebroid Invariants for Subgeometry / A.D. Blaom // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 21 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We investigate the infinitesimal invariants of an immersed submanifold Σ of a Klein geometry M ≅ G/H, and in particular an invariant filtration of Lie algebroids over Σ. The invariants are derived from the logarithmic derivative of the immersion of Σ into M, a complete invariant introduced in the companion article, A characterization of smooth maps into a homogeneous space. Applications of the Lie algebroid approach to subgeometry include a new interpretation of Cartan's method of moving frames and a novel proof of the fundamental theorem of hypersurfaces in Euclidean, elliptic, and hyperbolic geometry.
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| first_indexed | 2025-12-07T15:30:27Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-209788 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T15:30:27Z |
| publishDate | 2018 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Blaom, A.D. 2025-11-26T12:24:11Z 2018 Lie Algebroid Invariants for Subgeometry / A.D. Blaom // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 21 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 53C99; 22A99; 53D17 arXiv: 1703.03851 https://nasplib.isofts.kiev.ua/handle/123456789/209788 https://doi.org/10.3842/SIGMA.2018.062 We investigate the infinitesimal invariants of an immersed submanifold Σ of a Klein geometry M ≅ G/H, and in particular an invariant filtration of Lie algebroids over Σ. The invariants are derived from the logarithmic derivative of the immersion of Σ into M, a complete invariant introduced in the companion article, A characterization of smooth maps into a homogeneous space. Applications of the Lie algebroid approach to subgeometry include a new interpretation of Cartan's method of moving frames and a novel proof of the fundamental theorem of hypersurfaces in Euclidean, elliptic, and hyperbolic geometry. We thank Yuri Vyatkin for helpful discussions. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Lie Algebroid Invariants for Subgeometry Article published earlier |
| spellingShingle | Lie Algebroid Invariants for Subgeometry Blaom, A.D. |
| title | Lie Algebroid Invariants for Subgeometry |
| title_full | Lie Algebroid Invariants for Subgeometry |
| title_fullStr | Lie Algebroid Invariants for Subgeometry |
| title_full_unstemmed | Lie Algebroid Invariants for Subgeometry |
| title_short | Lie Algebroid Invariants for Subgeometry |
| title_sort | lie algebroid invariants for subgeometry |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/209788 |
| work_keys_str_mv | AT blaomad liealgebroidinvariantsforsubgeometry |