光滑映射到齐性空间的一个刻画
A Characterisation of Smooth Maps into a Homogeneous Space
摘要：
本文将流形上光滑映射的Cartan对数导数推广到李群$G$上，从而将光滑映射推广到齐性空间$M=G/H$上，并确定了从无穷小数据重构这类映射的整体单值性障碍.子流形$Σ\subset M$嵌入的对数导数在“克莱因几何”$M$的对称性下成为$Σ$的不变量，其分析在[SIGMA 14（2018），062，36 pages，arXiv：1703.03851]中进行。
英文摘要：
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 $Σ\subset M$ becomes an invariant of $Σ$ under symmetries of the "Klein geometry" $M$ whose analysis is taken up in [SIGMA 14 (2018), 062, 36 pages, arXiv:1703.03851].
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
