Название: Cut locus of a left invariant Riemannian metric on SO(3) in the axisymmetric case

Авторы: A. V. Podobryaev, Yu. L. Sachkov

Журнал: Journal of Geometry and Physics

Год: 2016

Том: 110

Страницы: 436–453

Образец цитирования:

A. V. Podobryaev, Yu. L. Sachkov, “Cut locus of a left invariant Riemannian metric on SO(3) in the axisymmetric case”, Journal of Geometry and Physics, 110 (2016), 436–453

Аннотация:

We consider a left invariant Riemannian metric on SO3 with two equal eigenvalues. We find the cut locus and the equation for the cut time. We find the diameter of such metric and describe the set of all most distant points from the identity. Also we prove that the cut locus and the cut time converge to the cut locus and the cut time in the sub-Riemannian problem on SO3 as one of the metric eigenvalues tends to infinity.