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

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

2006-10-02

arxiv.org/abs/math/0610070v1

Mathematics

Differential Geometry

39 pages, 5 figures

Scientific paper

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.

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