Chapter 16Differentiation and Integration on Smooth Manifolds
16.1 Exterior Derivatives
Let M be a smooth m‐manifold and recall that C∞(M) = Λ0(M) and
. The exterior derivative
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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