A Characterisation of Smooth Maps into a Homogeneous Space

Abstract

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].

References in corpus (3)

• Lectures on Integrability of Lie Brackets
• Conformal submanifold geometry I-III
• Lie Algebroid Invariants for Subgeometry

Cited by in corpus (1)

• Lie Algebroid Invariants for Subgeometry