Abstract
We prove that for n = 2, 3 any local homogeneous affine line field L; ⊂ Tℝn can be described by an affine line ℓ in an n-dimensional Lie algebra g, which means that L is diffeomorphic to the affine line field in a neighborhood of the identity of the Lie group of g obtained by pushing ℓ along the flows of left-invariant vector fields. We show that this statement does not hold for n = 4, for one of several types of homogeneous line fields.
The research was supported by the Israel Science Foundation grants 1383/07 and 510/12.
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Zhitomirskii, M. (2014). Homogeneous affine line fields and affine lines in Lie algebras. In: Stefani, G., Boscain, U., Gauthier, JP., Sarychev, A., Sigalotti, M. (eds) Geometric Control Theory and Sub-Riemannian Geometry. Springer INdAM Series, vol 5. Springer, Cham. https://doi.org/10.1007/978-3-319-02132-4_21
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DOI: https://doi.org/10.1007/978-3-319-02132-4_21
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-02131-7
Online ISBN: 978-3-319-02132-4
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