Chapter 16 Differentiation and Integration on Smooth Manifolds

16.1 Exterior Derivatives

Let M be a smooth m‐manifold and recall that C (M) = Λ0(M) and images . The exterior derivative images of Section 15.4 can therefore be expressed as


According to Theorem 15.4.6, d is linear and satisfies a type of product rule. In this section, we describe a generalization of d that has corresponding properties. Three equivalent approaches to this theory are available—axiomatic, local, and global.

We observe ...

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