A smooth manifold is a topological space locally homeomorphic to ℝⁿ with smoothly overlapping charts. Substrate for curvature, connection, and physical theories (GR, gauge theory).
Differential geometry (manifold)
Related concepts
- Topological space
- Coordinate geometry (Cartesian)
- Smooth manifold
- Banach manifold: charts into Banach spaces + Fréchet-derivative calculus
- Lie groups in physics
- Tensor analysis on manifolds
- Differential forms
- Membrane physics
- Levi-Civita Γ^k_{ij} = ½ g^{kl}(∂_i g_{jl}+∂_j g_{il}−∂_l g_{ij})
- Riemann R^ρ_{σμν}=∂_μΓ^ρ_{νσ}−∂_νΓ^ρ_{μσ}+ΓΓ−ΓΓ; (4,0) symmetries