Consider the left multiplication action of $SU(2)$ on $SU(4)$. My questions are: is $SU(2)$ a normal subgroup of $SU(4)?$ What is the quotient $SU(4)/SU(2)$? Is this a well known manifold?
2026-03-27 02:35:33.1774578933
Is the quotient $SU(4)/SU(2)$ a well known manifold?
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These are examples of coset manifolds actually $SU(2)$ is normal subgroup is not required, like you can construct $SO(3) /SO(2)$ which is just $S^2$.
If you ask how to calculate metric connection and scaler curvature etc. You can find in Arvanitoyeorgos - Intr to lie group and the geometry of homogeneous spaces Page 84 has example of the $S^2$ I talked about.
Hope this helps.
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