Category:Riemannian geometry

From Freepedia

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.

Subcategories

There are 2 subcategories to this category.

H

• Hyperbolic geometry

R

• Riemann surfaces

Articles in category "Riemannian geometry"

There are 63 articles in this category.

A Almost flat manifold B Bishop–Gromov inequality C Christoffel symbols Conformal map Cotton tensor Covariance and contravariance Covariant derivative Curvature Curvature of Riemannian manifolds Curvature tensor D De Sitter space E Einstein manifold Einstein notation 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

G cont. Gromov-Hausdorff convergence H Hodge dual Hodge theory Holonomy Hopf–Rinow theorem Hyperbolic 3-manifold J Jacobi field K Killing vector field Kähler manifold L Laplace operator Levi-Civita connection Lie derivative Line element 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