∇ connection, parallel transport. Geodesic ∇_γ' γ'=0. Exponential map. Hopf–Rinow.
graph TD
D1["Def: Connection ∇\n∇_X Y cov derivative"]
D2["Def: Parallel transport\n∇_γ' V=0"]
D3["Def: Geodesic\n∇_γ' γ'=0"]
D4["Def: Exp map\nexp_p v = γ(1)"]
T1["Thm: Geodesic eqn\nΓ-Christoffel"]
T2["Thm: Exp local diffeo\nnear 0"]
T3["Thm: Hopf–Rinow\ncompl⇔geod complete"]
T4["Thm: Gauss lemma\n〈exp'v,exp'w〉=〈v,w〉"]
T5["Thm: Jacobi fields\ngeod variation"]
D1 --> D2
D1 --> D3
D3 --> D4
D1 --> T1
D4 --> T2
D3 --> T3
T2 --> T4
classDef definition fill:#b197fc,color:#fff
classDef theorem fill:#51cf66,color:#fff
class D1,D2,D3,D4 definition
class T1,T2,T3,T4,T5 theorem
Process Statistics
- Nodes: 14
- Edges: 11
Frontier: math.DG