Tangent Space

★★★★☆Undergraduate

📖Definition

Vector space of all possible "directions" at a point on manifold

Tₚ M = γ'(0) : γ(0) = p

Dimension: dim Tₚ M = dim M

Basis: ∂/∂xⁱ |ₚ

예제 1

Tangent space of plane = ℝ²

예제 2

Tangent plane of sphere

Vector fields

Differential forms

Physics

#접공간#tangent#vector#manifold