Taylor polynomials on left-quotients of Carnot groups

TL;DR

This paper extends Taylor polynomial theorems to sub-Riemannian manifolds derived from Carnot groups, providing conditions for real analyticity and exploring L-harmonicity of these polynomials.

Contribution

It introduces Taylor polynomial theorems for sub-Riemannian manifolds as submetric images of Carnot groups, including analyticity and harmonicity conditions.

Findings

Established Taylor polynomial theorems for these manifolds

Provided a sufficient condition for real analyticity

Proved results on L-harmonicity of Taylor polynomials

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.