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

V. Gerdt·R. Horan·A. Khvedelidze·M. Lavelle·D. McMullan·Yu. Palii
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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.

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V. Gerdt, R. Horan, A. Khvedelidze, M. Lavelle, D. McMullan, Yu. Palii. 2005-11-24. On the Hamiltonian reduction of geodesic motion on SU(3) to SU(3)/SU(2). https://doi.org/10.1063/1.2358391

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