We prove the non-triviality of the Reeb flow for the standard contact spheres S 2n+1 , n = 3, inside the fundamental group of their contactomorphism group. The argument uses the existence of homotopically non-trivial 2-spheres in the space of contact structures of a 3-Sasakian manifold.
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Casals et al. (2014) studied this question.
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