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We call two Engel structures isotopic if they are homotopic through Engelstructures by a homotopy that fixes the characteristic line field. In thepresent paper we define an isotopy invariant of Engel structures on orientedcircle bundles over closed oriented three-manifolds and apply it to give anisotopy classification of Engel structures on circle bundles withcharacteristic line field tangent to the fibers.

Isotopy Classification of Engel Structures on Circle Bundles