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
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.