On the Hamiltonian reduction of geodesic motion on SU(3) to SU(3)/SU(2)

The reduced Hamiltonian system on T*SU(3)/SU(2)) is derived from a Riemannian geodesic motion on the SU(3) group manifold parameterised by the generalised Euler angles and endowed with a bi-invariant metric. Our calculations show that the metric defined by the derived reduced Hamiltonian flow on the orbit space SU(3)/SU(2)=S^5 is not isometric or even geodesically equivalent to the standard Riemannian metric on the five-sphere S^5 embedded into R^6.