An Introduction to Manifolds pp 273-316 | Cite as
De Rham Theory
Chapter
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Abstract
By the fundamental theorem for line integrals (Theorem 23.13), if a smooth vector field F is the gradient of a scalar function f, then for any two points p and q in \(\mathbb{R}^{3}\), the line integral \(\int_{c}\mathbf{F} \cdot \) d r can be computed in terms of its values at the two endpoints as f (q)- f (p).
Keywords
Exact Sequence Differential Form Cohomology Class Homotopy Type Cochain Complex
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© Springer Science+Business Media, LLC 2011