User:PtolRek/Books/DG.004

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DG.004

Fundamental notions: Metric tensor; Riemannian manifold; Pseudo-Riemannian manifold; Levi-Civita connection
Non-Euclidean geometry: Non-Euclidean geometry; Elliptic geometry; Spherical geometry; Sphere-world; Angle excess; Hyperbolic geometry; Hyperbolic space; Hyperboloid model; Poincaré disc model; Poincaré half-plane model; Poincaré metric; Angle of parallelism
Geodesic: Geodesic; Prime geodesic; Geodesic flow; Exponential map; Injectivity radius; Geodesic deviation equation; Jacobi field
Symmetric spaces: Riemannian symmetric space; Space form; Constant curvature; Taut submanifold; Uniformization theorem; Myers theorem; Gromov's compactness theorem
Riemannian submanifolds: Riemannian submanifold; Gauss-Codazzi equations; Darboux frame; Hypersurface; Induced metric; Nash embedding theorem; Minimal surface; Helicoid; Catenoid; Costa's minimal surface; Hsiang-Lawson's conjecture
Curvature of Riemannian manifolds: Curvature of Riemannian manifolds; Theorema Egregium; Gauss-Bonnet theorem; Chern-Gauss-Bonnet theorem; Chern-Weil homomorphism; Gauss map; Second fundamental form; Curvature form; Curvature tensor; Geodesic curvature; Scalar curvature; Sectional curvature; Ricci curvature; Ricci flat; Ricci decomposition; Schouten tensor; Weyl curvature; Ricci flow; Einstein manifold; Holonomy
Theorems in Riemannian geometry: Hopf-Rinow theorem; Cartan-Hadamard theorem; Rauch comparison theorem; Synge theorem; Toponogov theorem; Sphere theorem; Hodge theorem; Yamabe problem