SUB-RIEMANNIAN GEODESICS ON THE THREE-DIMENSIONAL SOLVABLE NON-NILPOTENT LIE GROUP SOLV~-

摘要

In this paper we study geodesics of a left-invariant sub-Riemannian metric on a three-dimensional solvable Lie group. A system of differential equations for geodesics is derived from Pontryagin maximum principle and by using Hamiltonian structure. In a generic case the normal geodesies are described by elliptic functions, and their qualitative behavior is quite complicated.