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Dec 1, 2020 at 17:46 comment added Andy Sanders Your argument is a little garbled to me, but the fact is true: a connection preserving a sub-bundle is the same as the corresponding principal connection restricting to the filtered frame bundle. I suggest you write the meaning of these things out in local coordinates to really get a feel for what is going on.
Nov 30, 2020 at 19:46 history answered Jon Aycock CC BY-SA 4.0