# When does the normal bundle of a submanifold of $R^n$ admit a flat connection?
Given a smooth submanifold of $R^n$, I was wondering if there is a reasonably simple criterion for deciding whether its normal bundle admits a flat connection. I am not ruling out monodromy in the statement of the question (thus for example, a Moebius strip immersed in $R^3$ fits the bill.)