A PDE-free geometric decomposition splits force fields in arbitrary dimensions into exact gradient and antiexact generalized-curl components via homotopy operators on star-shaped domains, with the antiexact part further resolved by the Frobenius theorem into integrable potentials and a path-obstruct
Thirring, A Course in Mathematical Physics 1 and 2 , Springer-Verlag New York Inc
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Decomposition and characterization of curl forces for all space dimensions
A PDE-free geometric decomposition splits force fields in arbitrary dimensions into exact gradient and antiexact generalized-curl components via homotopy operators on star-shaped domains, with the antiexact part further resolved by the Frobenius theorem into integrable potentials and a path-obstruct