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.