Abstract
Let G be a Lie transformation group on a manifold M. Then a map f: N→G is differentiable, iff for every point p∈M the map q↦ f(q)·p is differentiable.
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References
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Linden, M., Reckziegel, H. On the differentiability of maps into Lie transformation groups. Manuscripta Math 63, 377–379 (1989). https://doi.org/10.1007/BF01168378
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DOI: https://doi.org/10.1007/BF01168378