A nice example is the Hopf fibration: $S^1 \subset C$ acts on $S^3\subset \mathbb C^2$ by scalar multiplication. The quotient is $\mathbb CP^1.$ Of course there are various generalizations.
A nice example is the Hopf fibration: $S^1 \subset C$ acts on $S^3\subset C^2$ by scalar multiplication. The quotient is $CP^1.$ Of course there are various generalizations.