Concept

Differential ideal

Summary
In the theory of differential forms, a differential ideal I is an algebraic ideal in the ring of smooth differential forms on a smooth manifold, in other words a graded ideal in the sense of ring theory, that is further closed under exterior differentiation d, meaning that for any form α in I, the exterior derivative dα is also in I. In the theory of differential algebra, a differential ideal I in a differential ring R is an ideal which is mapped to itself by each differential operator. Exterior differential systems and partial differential equations An exterior differential system consists of a smooth manifold M and a differential ideal : I\subset \Omega^*(M) . An integral manifold of an exterior differential system (M,I) consists of a submanifold N\subset M having the property that the pullback to N of all differential forms contained in I vanishes identically. One can express any partial di
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