A vector field is a section of its tangent bundle, meaning that to every point 
in a manifold 
, a vector 
is associated, where 
is the tangent space.
Tangent Bundle Section
See also
Tangent Bundle, Tangent SpaceExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Tangent Bundle Section." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/TangentBundleSection.html