Differentiation Of Differental Forms

Statements

Definition (@Bac12, pp. 74). Let $\omega$ be an $n-$differential form, and $v_1,\dots ,v_{n+1}$ be $n+1$ vector fields. The operator

$$\begin{array}{rclc}d:& \mathbb{R}& \to & \mathbb{R}\\ & \omega (v_1,\dots ,v_{n+1})& \mapsto & \sum _{i=1}^{n+1}(-1{)}^{i+1}\frac{\partial \omega }{\partial v_i}(v_1,\dots ,v_{i-1},v_{i+1},\dots ,v_{n+1})\end{array}$$

is said to be a differential operator.

Results

Properties of Differentiation

Examples

Example - Differentiation of a Differential Form

example_5.6