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

Abstract

We consider a left invariant Riemannian metric on SO(3) 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 SO(3) as one of the metric eigenvalues tends to infinity.

29 pages, 6 figures, corrected typos

Cited by in corpus (10)

• Quantum Computational Complexity -- From Quantum Information to Black Holes and Back
• On the subRiemannian cut locus in a model of free two-step Carnot group
• The smallest Laplace eigenvalue of homogeneous 3-spheres
• Diameter of $S{U}_2$ for a left-invariant axisymmetric Riemannian metric
• Symmetric Riemannian problem on the group of proper isometries of hyperbolic plane
• Homogeneous geodesics in sub-Riemannian geometry
• Diameter and Laplace eigenvalue estimates for left-invariant metrics on compact Lie groups
• Conjugate points for systems of second-order ordinary differential equations
• Symmetries in left-invariant optimal control problems
• Left-invariant optimal control problems on Lie groups