The cotangent bundle 
of a smooth manifold 
is the disjoint union of its cotangent spaces 
. Its elements are pairs 
, where 
and 
is a cotangent vector
at 
,
meaning a linear functional on the tangent
space 
.
Cotangent Bundle
See also
Cotangent Space, Cotangent Vector, Dual Vector Space, Tangent Bundle, Tangent SpaceExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Cotangent Bundle." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/CotangentBundle.html