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Deformation of morphisms along leaves of foliations define the tangentialfoliation on the corresponding space of morphisms. We prove that codimensionone fo-liations having a tangential foliation with at least one non-algebraicleaf are transversely homogeneous with structure group determined by thecodimension of the non-algebraic leaf in its Zariski closure. As anapplication, we provide a structure theorem for degree three foliations on$P^3$ .

Deformation of Rational Curves Along Foliations