Thread: Frame bundle
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Mar8-12, 07:47 PM
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Quote Quote by Matterwave View Post
Can you explain a little more your last sentence regarding "when the bundle is a vector bundle..."? Can vector bundles be principle bundles?
Oh, sorry. All along I wrote about principal bundles because that is what you seem to be interested in primarily, but actually this definition of connection holds for a general fiber bundle. And while I agree that a vector bundle cannot be a principal bundle, a vector bundle is always a fiber bundle, so this definition of connection in terms of horizontal subbundle applies to it. This is what I had in mind when I wrote that awkward last comment.