I´m actually working with principal bundles and I´m looking for particular examples. For instance, a principal bundle of structure group $Gl(n)$ is just a vector bundle. I´m wondering what happens if we consider for instance $G=\mathbb{G}_{a}$ the additive group. What is a principal bundle of structure group $\mathbb{G}_{a}$? Is there any relation with principal bundles over projective spaces? Thank you for your time

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    $\begingroup$ Isn't the multiplicative group just $\mathrm{GL}(1)$? So, it should just give you line bundles. $\endgroup$
    – Mohan
    Apr 10, 2020 at 14:40
  • $\begingroup$ Sorry, I wanted to say the additive group $\endgroup$ Apr 10, 2020 at 14:59


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