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| Summary: | 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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| ISSN: | 1815-0659 |