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Sep 5, 2011 at 13:23 comment added marc So the flows that are dual to the pull backs of the connection 1 form are Lie brackets of orthonormal frames. Given any vector field one obtains a flow by your construction - assuming that you have a conformal structure.Yes? How does this restrict the possible flows - if at all? I guess an equivalent way to ask this question is to start with a vector field and ask for another field that is parallel along it.
Sep 4, 2011 at 12:49 vote accept marc
Aug 21, 2011 at 22:21 history answered Robert Bryant CC BY-SA 3.0