On the differentiability of maps into Lie transformation groups. (English) Zbl 0672.57027
Summary: Let G be a Lie transformation group on a manifold M. Then a map f: \(N\to G\) is differentiable iff for every point \(p\in M\) the map \(q\mapsto f(q)\cdot p\) is differentiable.
MSC:
| 57S99 | Topological transformation groups |
References:
| [1] | Greub,W./Halperin,S./Vanstone,R. Connections. curvature, and cohomology. Vol.II. London: Academic Press 1973 · Zbl 0335.57001 |
| [2] | Kobayashi, S.: Transformation groups in differential geometry. Berlin-Heidelberg-New York, Springer 1972 · Zbl 0246.53031 |
| [3] | Palais. R. S.: A global formulation of Lie theory of transformation groups. Memoirs of the Amer.Math.Soc.22(1957) · Zbl 0178.26502 |
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