Lie Algebroid Invariants for Subgeometry

Symmetry Integrability and Geometry-Methods and Applications

article

Anthony D. Blaom¹ 

[1] Waiheke Island

关键词: subgeometry;    Lie algebroids;    Cartan geometry;    Klein geometry;    differential invariants;   

DOI  :  10.3842/SIGMA.2018.062

来源: National Academy of Science of Ukraine

【 摘 要 】

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.

【 授权许可】

Unknown