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Contact structures and Beltrami fields on the torus and the sphere
We show the existence of overtwisted contact structures on the (round) 3-sphere and the (flat) 3-torus for which the ambient metric is weakly compatible.Our proofs are based on the construction of S 1 -invariant nonvanishing curl eigenfields on S 3 and T 3 using suitable families of Jacobi polynomials and …