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
Date:2018
Main Author: Blaom, A.D.
Format: Article
Language:English
Published: Інститут математики НАН України 2018
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
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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.
first_indexed 2025-12-07T15:30:27Z
format Article
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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