g Riemannian metric. Riemann curvature R, Ricci, scalar. Sectional curvature. Gauss–Bonnet.
graph TD
D1["Def: Riemannian g\npos def on T_p"]
D2["Def: Levi-Civita\nunique metric conn"]
D3["Def: Riem curvature\nR(X,Y)Z"]
D4["Def: Sectional K\nK(σ) plane"]
T1["Thm: Levi-Civita exists\n∇g=0, torsion-free"]
T2["Thm: Ricci, scalar\nRic, R from R"]
T3["Thm: Gauss eqn\nembedd curvature"]
T4["Thm: Gauss–Bonnet\n∫K dA = 2πχ"]
T5["Thm: Constant curv\nspace forms"]
D1 --> T1
D2 --> D3
D3 --> T2
D4 --> T3
T2 --> T4
T4 --> T5
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: 15
- Edges: 12
Frontier: math.DG