Affine bundle

In mathematics, an affine bundle is a fiber bundle whose typical fiber, fibers, trivialization morphisms and transition functions are affine.

Let ${\displaystyle {\overline {\pi }}:{\overline {Y}}\to X}$ be a vector bundle with a typical fiber a vector space ${\displaystyle {\overline {F}}}$. An affine bundle modelled on a vector bundle ${\displaystyle {\overline {\pi }}:{\overline {Y}}\to X}$ is a fiber bundle ${\displaystyle \pi :Y\to X}$ whose typical fiber ${\displaystyle F}$ is an affine space modelled on ${\displaystyle {\overline {F}}}$ so that the following conditions hold:

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