Projective bundle

In algebraic geometry and differential geometry, a projective bundle is a space that parametrizes lines (or higher-dimensional projective subspaces) in a vector bundle. More formally, given a vector bundle \( E \) over a topological space (or algebraic variety) \( X \), the projective bundle associated with \( E \) is denoted by \( \mathbb{P}(E) \) and consists of the projectivization of the fibers of \( E \).