Geodesics and shortest arcs of a special sub-Riemannian metric on the Lie group SL(2)

Abstract

The authors found geodesics, shortest arcs, cut loci, and conjugate sets for some leftinvariant sub-Riemannian metric on the Lie group SL(2) that is right-invariant relative to the Lie subgroup SO(2) ⊂ SL(2) (in other words, for invariant sub-Riemannian metric on weakly symmetric space (SL(2) × SO(2))/SO(2)).