In differential geometry, Riemannian geometry is the study of smooth manifolds with Riemannian metrics; i.e. a choice of positive-definite quadratic form on a manifold's tangent spaces which varies smoothly from point to point. This gives in particular local ideas of angle, length of curves, and volume. From those some other global quantities can be derived, by integrating local contributions.

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R

• Riemann surfaces

Articles in category "Riemannian geometry"

There are 59 articles in this category.

Almost flat manifold B Bishop-Gromov inequality C Christoffel symbols Conformal map Cotton tensor Covariant derivative Curvature Curvature of Riemannian manifolds Curvature tensor E Einstein manifold Exponential map F Fundamental theorem of Riemannian geometry G Gauss map Geodesic Geodesic curvature Geometrization conjecture Glossary of Riemannian and metric geometry Gromov's compactness theorem Gromov-Hausdorff convergence

H Hodge dual Hodge theory Holonomy Hopf-Rinow theorem Hyperbolic 3-manifold Hyperbolic space J Jacobi field K Killing vector field Kähler manifold L Levi-Civita connection Lie derivative M Metric tensor Myers theorem N Nash embedding theorem P Parallel transport Poincaré half-plane model Poincaré metric Pseudo-Riemannian manifold R Ricci curvature Ricci flow

R cont. Ricci-flat manifold Riemannian geometry Riemannian manifold Riemannian submanifold Riemannian symmetric space S Scalar curvature Second fundamental form Sectional curvature Seifert-Weber space Soul theorem Space form Spherical 3-manifold Splitting theorem Sub-Riemannian manifold T Theorema Egregium Thurston elliptization conjecture Torsion Trace-free Ricci tensor U Uniformization theorem W Weyl curvature