# Category:Differential Forms

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This category contains results about **Differential Forms**.

Definitions specific to this category can be found in **Definitions/Differential Forms**.

Let $M$ be an $n$-dimensional $C^1$ manifold.

Let $\ds \Lambda^k T^* M = \bigcup_{p \mathop \in M} \set p \times \map {\Lambda^k} {T_p^*M}$, endowed with its natural structure as a $C^0$ manifold.

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A **differential $k$-form** is a continuous mapping:

- $\omega : M \to \Lambda^kT^* M$

satisfying:

- $\forall p \in M \map {\paren {\pi \circ \omega} } p = p$

where $\pi : \Lambda^k T^*M \to M$ is the projection onto the first argument, defined by:

- $\map \pi {p, v} = p$

In other words, a **differential form** is a continuous mapping $\omega$ that assigns each point $p \in M$ an alternating $k$-form $\map \omega p$ on $T_p M$.

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