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A Characterisation of Smooth Maps into a Homogeneous Space
Symmetry, integrability and geometry: methods and applications, Tome 18 (2022) Cet article a éte moissonné depuis la source Math-Net.Ru

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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].
Keywords: homogeneous space, subgeometry, Cartan geometry, Klein geometry, logarithmic derivative, Darboux derivative, differential invariants.
Mots-clés : Lie algebroids 
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     author = {Anthony D. Blaom},
     title = {A {Characterisation} of {Smooth} {Maps} into a {Homogeneous} {Space}},
     journal = {Symmetry, integrability and geometry: methods and applications},
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     volume = {18},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2022_18_a28/}
}
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Anthony D. Blaom. A Characterisation of Smooth Maps into a Homogeneous Space. Symmetry, integrability and geometry: methods and applications, Tome 18 (2022). http://geodesic.mathdoc.fr/item/SIGMA_2022_18_a28/

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