Taylor polynomials on left-quotients of Carnot groups

Abstract

We prove classical Taylor polynomial theorems for sub-Riemannian manifolds that are obtained as the submetric image of a Carnot group. For these theorems we also prove a sufficient condition for real analyticity and a result on L-harmonicity of Taylor polynomials.

This new version changed the definition of Taylor polynomials and we prove equivalence with the old definition. We added details to the proofs of main theorems