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for questions about fiber bundles, including structure groups, principal bundles, and spaces of sections.
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How to find $\beta^\prime_e(t)$ where $\beta_e(t)=\textrm{Hol}^\sigma_{\gamma_{1, t}}(e)$?
Let $p:E\longrightarrow B$ be a surjective submersion and $\sigma: p^*(TB)\longrightarrow TE$ a complete connection. Given a path $\gamma: [a, b]\longrightarrow B$ and $s, t\in [a, b]$ such that $s<t$ …