tangentsystem
The tangentsystem is a concept used in mathematics, particularly in differential geometry, to refer to the system of tangent vectors attached to points of a space or to the space of all such vectors. In English-language literature the term is uncommon; more standard terminology is tangent space at a point or tangent bundle. The expression is sometimes encountered in German-language texts (Tangentsystem) or used descriptively to describe the collection of tangent directions across a manifold.
Formally, for a smooth manifold M, the tangent space at a point p ∈ M, denoted T_pM, is
Examples help illustrate the idea: for M = R^n, T_pR^n ≅ R^n, and the tangent vectors are simply
Applications of the tangentsystem include the linear approximation of manifolds, the definition of vector fields and