Suppose $S$ is a Riemann Surface and $M$ is given as a $\mathbb{C} \mathbb{P} (1)-$bundle over $S$ where $ \pi:M \longrightarrow S$ is the corresponding projection.
Is not the previous statement (stated above) equivalent to saying that $(M, \pi, S, \mathbb{C} \mathbb{P} (1))$ is a Fibre Bundle?