Smooth mappings between foliated manifolds

Abstract

In [-1], L. A. Favaro has presented the notion of stability in the tangential sense of smooth mappings between foliated manifolds. Moreover he has presented the notion of infinitesimal stability in the tangential sense in order to characterize the former. In fact, he has shown that the latter is the sufficient condition of the former. In this paper, we shall prove that the converse of Favaro's theorem is true for foliation preserving mappings. The key point of the proof is a transversality theorem in some sense. We shall call it "the transversality theorem in the tangential sense". In w we will formulate the main result. The transversality theorem in the tangential sense will be given and proved in w We will prove the main theorem in w All manifolds, foliations and mappings considered here are differentiable of class C ~. All manifolds should satisfy the second countability axiom.