Surfaces Which Behave Like Vortex Lines

摘要

In general setting of theory of integral invariants, due to Poincaré and Cartan, one can find a d-dimensional integrable distribution (given by a possibly higher-rank form) whose integral surfaces behave like vortex lines: they move with (abstract) fluid. Moreover, in a special case they reduce to true vortex lines and, in this case, we get the celebrated Helmholtz theorem.