Covector Field

Statements

Definition. (Tu11, pp. 34) A covector field or a differential 1-form on an open subset $U\subset {\mathbb{R}}^n$ is a function $\omega$ that assigns to each point $p\in U$ a covector ${\omega }_p\in T_p^{\ast }({\mathbb{R}}^n),$

$$\begin{array}{rrcl}\omega :& U& \to & \bigcup _{p\in U}{T}_p^{\ast }({\mathbb{R}}^n)\\ & p& \mapsto & {\omega }_p\in T_p^{\ast }({\mathbb{R}}^n).\end{array}$$