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The diffeomorphism group of a Lie foliation

Gilbert Hector; Enrique Macías-Virgós; Antonio Sotelo-Armesto — 2011

Annales de l’institut Fourier

We describe explicitly the group of transverse diffeomorphisms of several types of minimal linear foliations on the torus $T^{n}$ , $n \geq 2$ . We show in particular that non-quadratic foliations are rigid, in the sense that their only transverse diffeomorphisms are $\pm Id$ and translations. The description derives from a general formula valid for the group of transverse diffeomorphisms of any minimal Lie foliation on a compact manifold. Our results generalize those of P. Donato and P. Iglesias for $T^{2}$ , P. Iglesias and...

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