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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| Published in | Symmetry, integrability and geometry, methods and applications Vol. 14 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Kiev
National Academy of Sciences of Ukraine
18.06.2018
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| Subjects | |
| Online Access | Get full text |
| ISSN | 1815-0659 1815-0659 |
| DOI | 10.3842/SIGMA.2018.062 |
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| Abstract | 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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| AbstractList | 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. |
| Author | Blaom, Anthony D. |
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| ContentType | Journal Article |
| Copyright | 2018. This work is published under http://creativecommons.org/licenses/by-sa/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. |
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| Title | Lie Algebroid Invariants for Subgeometry |
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