DIFFEOMORPHISMS CONFORMAL ON DISTRIBUTIONS

Abstract. Let f: M → N be a local diffeomorphism between Riemannian manifolds M and N. We define the eigenvalues of f as the eigenvalues of self-adjoint and positive definite operator df∗df: TM → TM, where df ∗ denotes the operator adjoint to df. If f is conformal on a distribution D, then dimVλ ≥ 2 dimD − dimM, where Vλ is the eigenspace of f corresponding to coefficient of conformality λ. Moreover, if f has distinct eigenvalues, then there is locally a k–dimensional distribution D such that f is conformal on D if and only if k < (dimM + 1)/2