Let 
be a point in an 
-dimensional compact manifold 
, and attach at 
a copy of 
tangential to 
. The resulting structure is called the tangent space of 
at 
and is denoted 
. If 
is a smooth curve passing through 
, then the derivative of 
at 
is a vector in 
.
Tangent Space
See also
Chart Tangent Space, Submanifold Tangent Space, Tangent, Tangent Bundle, Tangent Plane, Tangent Vector Explore this topic in the MathWorld classroomExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Tangent Space." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/TangentSpace.html