If a vector field $\boldsymbol F(\boldsymbol x)$ is given where $\boldsymbol x$ is a given position point in an $n$-dimensional space and $\boldsymbol F$ is the velocity vector (Of course in the same dimensions).
Then, for any given arbitrary point $\boldsymbol x_0$, is there a closed hyper-surface $S$ (with $n-1$ dimensions) that
crosses $\boldsymbol x_0$
contains origin inside
is perpendicular to $\boldsymbol F(\boldsymbol x)$ everywhere on the surface.
?
How to check if this surface exists?
How to obtain this surface analytically?
I am after a solution that works for all fields and not a specific case.
