Suppose I have a vector field $v$, and I am interested in knowing whether it is a potential gradient, i.e. $v = \nabla f$ for some scalar function $f$. Symmetry of the Jacobian $Dv$ is clearly necessary for this function to be a Hessian-- is this condition also sufficient for $v$ to be a gradient? (At least locally over some finite domain.)
2026-03-27 05:38:16.1774589896
If the Jacobian of a vector field is symmetric, is the vector field a gradient?
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