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Results tagged with principal-bundles
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user 68927
A principal $G$-bundle, where $G$ denotes any topological group, is a fiber bundle $\pi :P → X$ together with a continuous right action $P × G → P$ such that $G$ preserves the fibers of $P$ and acts freely and transitively on them.
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Extrinsic horizontal path lifting
As a follow up question to my previous question about the orthonormal frame bundle, I would like to understand a simple example explicitly.
Let $\mathbb{S}^2$ be written extrinsically as $$\mathbb{S …
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Extrinsic horizontal path lifting
So I think I have an answer, but instead of using the ODE in Step 3, it uses a simpler equation that implies it: $$ \dot{w} = \tilde{\gamma}^{-1}\dot{\gamma}\,. $$
Here $w:[0,1]\to\mathbb{R}^2$ is a …
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