Anisotropic quaternion Carnot groups: geometric analysis and Green's function

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

We construct examples of 2-step Carnot groups related to quaternions and study their fine structure and geometric properties. This involves the Hamiltonian formalism, which is used to obtain explicit equations for geodesics and the computation of the number of geodesics joining two different points on these groups. We able to find the explicit lengths of geodesics. We present the fundamental solutions of the Heat and sub-Laplace equations for these anisotropic groups and obtain some estimates for them, which may be useful.
39 pages, 5 figures

Keywords

Differential Geometry, 53C17, 53C22, 35H20

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/117789

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0610070
 http://arxiv.org/abs/math/0610070

Collections

arXiv