Differential Geometry
The notion of a differential motivates several concepts in differential geometry (and differential topology).
- Differential forms provide a framework which accommodates multiplication and differentiation of differentials.
- The exterior derivative is a notion of differentiation of differential forms which generalizes the differential of a function (which is a differential 1-form).
- Pullback is, in particular, a geometric name for the chain rule for composing a map between manifolds with a differential form on the target manifold.
- Covariant derivatives or differentials provide a general notion for differentiating of vector fields and tensor fields on a manifold, or, more generally, sections of a vector bundle: see Connection (vector bundle). This ultimately leads to the general concept of a connection.
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