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We prove that a closed 3-dimensional manifold is a torus bundle over the circle if and only if it carries a closed nonsingular 1-form which is linearly deformable into contact forms.
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Hamidou Dathe and Philippe Rukimbira, “Fibrations and contact structures,” International Journal of Mathematics and Mathematical Sciences, vol. 2005, no. 4, pp. 555-560, 2005. doi:10.1155/IJMMS.2005.555
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