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arXiv · 1703.03851

Lie Algebroid Invariants for Subgeometry

Anthony D. Blaom
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Abstract

We investigate the infinitesimal invariants of an immersed submanifold $Σ$ of a Klein geometry $M\cong G/H$, 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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Anthony D. Blaom. 2018-06-18. Lie Algebroid Invariants for Subgeometry. https://doi.org/10.3842/sigma.2018.062

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