if a non-zero vector field $v$ on surface $S$ has its covariant differential $Dv=0$, then what do we know about the Gauss curvature $K$ of $S$?
I guess we can deduce that $K=0$ according to Gauss-Bonnet formula, but I don't know how to do that.
2026-04-03 22:29:49.1775255389
Questions on Covariant differential and Gauss curvature
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