Induced subbundles and Nash's implicit function theorem

Abstract

Given two manifolds X and Y and smooth subbundles S ⊂ T( X) and T ⊂ T( Y), we study C ∞-maps ƒ : X → Y which induce S from T. Our study relies on Nash–Gromov implicit function theorem. We show that, under certain non-degeneracy conditions, the (nonlinear differential) operator D T : ƒ → S = ƒ ∗( T) is an open map. Moreover, under some additional topological restriction on X, we establish the existence of maps ƒ inducing S from T.