Definition:Transitive Group Action on Fibers
Let $\tilde M$, $M$ be smooth manifolds.
Let $\pi : \tilde M \to M$ be a smooth submersion.
Let $p,q \in \tilde M$ be base points such that $\map \pi p = \map \pi q$.
Let $G$ be a group.
- $\exists \phi \in G : \phi \cdot p = q$
Then the group action is said to be transitive on fibers.