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

TL;DR

This paper derives a reduced Hamiltonian system from geodesic motion on SU(3) and finds that its metric on the orbit space differs from the standard metric on S^5, revealing new geometric insights.

Contribution

It provides a detailed derivation of the reduced Hamiltonian on SU(3)/SU(2) and compares its metric to the standard one on S^5, showing they are not isometric.

Findings

The reduced Hamiltonian system is explicitly derived.

The metric on the orbit space differs from the standard S^5 metric.

The reduced metric is not isometric or geodesically equivalent to the standard metric.

Abstract

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.