A Characterisation of Smooth Maps into a Homogeneous Space

Symmetry Integrability and Geometry-Methods and Applications

article

Anthony D. Blaom¹ 

[1] University of Auckland

关键词: homogeneous space;    subgeometry;    Lie algebroids;    Cartan geometry;    Klein geometry;    logarithmic derivative;    Darboux derivative;    differential invariants.;   

DOI  :  10.3842/SIGMA.2022.029

来源: National Academy of Science of Ukraine

【 摘 要 】

We generalize Cartan's logarithmic derivative of a smooth map from a manifold into a Lie group $G$ to smooth maps into a homogeneous space $M=G/H$, and determine the global monodromy obstruction to reconstructing such maps from infinitesimal data. The logarithmic derivative of the embedding of a submanifold $\Sigma \subset M$ becomes an invariant of $\Sigma $ under symmetries of the ''Klein geometry'' $M$ whose analysis is taken up in [SIGMA 14 (2018), 062, 36 pages, arXiv:1703.03851].

【 授权许可】

Unknown