A covector field \(\omega\) is called smooth if \(\omega\) is smooth as a map between the smooth manifold \(M\) and its cotangent bundle \(T^*M\).

It is denoted by \(\mathfrak{X}^*(M)\).

Examples Link to heading

• differentiation of a real-valued function

See also Link to heading

• line integrals of smooth covector fields
• exact covector field
• conservative covector field
• closed covector field