Lie Algebroid Invariants for Subgeometry

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.

References in corpus (5)

• Lectures on Integrability of Lie Brackets
• Conformal submanifold geometry I-III
• Cartan Connections on Lie Groupoids and their Integrability
• A Characterisation of Smooth Maps into a Homogeneous Space
• The Lie algebroid associated with a hypersurface

Cited by in corpus (2)

• The Lie algebroid associated with a hypersurface
• A Characterisation of Smooth Maps into a Homogeneous Space