At each point p of a smooth n-manifold, an n-dimensional vector space of derivations C^∞(M)→ℝ at p (equivalently, equivalence classes of curves through p).
Tangent space T_p M
Related concepts
- Smooth manifold
- Vector space
- Derivative
- Vector field
- Differential form
- Morse theory: critical-point indices, handle-attachment, Morse inequalities
- Jet bundle J^k(M,N): truncated Taylor fibre + prolongation functor
- 2-jet of x³: j²(0)=(0,0,0); j²(1)=(1,3,6); j²(2)=(8,12,12)
- Riemann R^ρ_{σμν}=∂_μΓ^ρ_{νσ}−∂_νΓ^ρ_{μσ}+ΓΓ−ΓΓ; (4,0) symmetries