# Category:Definitions/Differential Forms

Jump to navigation
Jump to search

This category contains definitions related to Differential Forms.

Related results can be found in **Category: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.

This article, or a section of it, needs explaining.In particular: What is $\map {\Lambda^k} {T_p^*M}$?You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by explaining it.To discuss this page in more detail, feel free to use the talk page.When this work has been completed, you may remove this instance of `{{Explain}}` from the code. |

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 $T_p M$.

## Pages in category "Definitions/Differential Forms"

The following 2 pages are in this category, out of 2 total.