Let $\pi : P \rightarrow M$ be a principal $G$ bundle. Suppose $R_{g}: P \rightarrow P$ is a smooth map induced by the smooth right $G$ action on $P$. Is $ R_{g} $ a smooth submersion for all $g \in G $ ?
2026-03-25 00:06:36.1774397196
Is $G$ action on a principal bundle a smooth submersion?
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