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Integral manifold


In mathematics, certain systems of partial differential equations are usefully formulated, from the point of view of their underlying geometric and algebraic structure, in terms of a system of differential forms. The idea is to take advantage of the way a differential form restricts to a submanifold, and the fact that this restriction is compatible with the exterior derivative. This is one possible approach to certain over-determined systems, for example. A Pfaffian system is specified by 1-forms alone, but the theory includes other types of example of differential system.

Given a collection of differential 1-forms on an -dimensional manifold , an integral manifold is a submanifold whose tangent space at every point is annihilated by each .


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