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$TSU(n)$ completely integrable with 3 $SU(2)$ invariant functions?
Consider the Lie group $SU(n)$ endowed with the standard bi-invariant metric. Then $SU(n)$ can be viewed as a symmetric space of $K_{n,n} := SU(n) \times SU(n)$.
Define $M := K_{n,n} /SU(n)$. Using ...
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