Definition:Transition Mapping

Definition

Let $B = \struct {E, M, \pi, F}$ be a fiber bundle.

Let $\struct {U, \chi}$, $\struct {V, \xi}$ be two local trivializations with $U \cap V \ne \O$.

Then the mapping:

$\xi \circ \chi^{-1} : U \cap V \times F \to U \cap V \times F$

is called a transition mapping from $\struct {U, \chi}$ to $\struct {V, \xi}$.

Sources

• 2013: Gerd Rudolph and Matthias Schmidt: Differential Geometry and Mathematical Physics: $\S 2.2$: Remark $2.2.2 \ / \ 2$