A vector field \(X\colon M\to TM\) on a smooth manifold \(M\) is called smooth if \(X\) is smooth as a map between the smooth manifold \(M\) and its tangent bundle \(TM\).

The set of vector fields on \(M\) is denoted by \(\mathfrak{X}(M)\).

Links Link to heading

• smooth map between manifolds
• vector field
• tangent bundle
• trajectory of a vector field
• smooth covector field
• smooth tensor field