Lie Algebroid Invariants for Subgeometry

We investigate the infinitesimal invariants of an immersed submanifold $\Sigma $ of a Klein geometry $M\cong G/H$, and in particular an invariant filtration of Lie algebroids over $\Sigma $. The invariants are derived from the logarithmic derivative of the immersion of $\Sigma $ into $M$, a complete...

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Bibliographic Details
Published inSymmetry, integrability and geometry, methods and applications Vol. 14
Main Author Blaom, Anthony D.
Format Journal Article
LanguageEnglish
Published Kiev National Academy of Sciences of Ukraine 18.06.2018
Subjects
Euclidean geometry
Geometry
Invariants
Manifolds (mathematics)
Online AccessGet full text
ISSN1815-0659
1815-0659
DOI10.3842/SIGMA.2018.062

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Summary:We investigate the infinitesimal invariants of an immersed submanifold $\Sigma $ of a Klein geometry $M\cong G/H$, and in particular an invariant filtration of Lie algebroids over $\Sigma $. The invariants are derived from the logarithmic derivative of the immersion of $\Sigma $ 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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content type line 14
ISSN:1815-0659
1815-0659
DOI:10.3842/SIGMA.2018.062