Category:Riemannian geometry
Wikimedia Commons has media related to Riemannian geometry.
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
This category has the following 9 subcategories, out of 9 total.
- Riemannian manifolds (39 P)
- Theorems in Riemannian geometry (21 P)
C
G
- Geodesic (mathematics) (19 P)
- Geometric flow (9 P)
H
- Hodge theory (15 P)
S
Σ
- Riemannian geometry stubs (44 P)
Pages in category "Riemannian geometry"
The following 140 pages are in this category, out of 140 total. This list may not reflect recent changes.
C
- Calculus of moving surfaces
- Calibrated geometry
- Cartan–Ambrose–Hicks theorem
- Cartan–Hadamard conjecture
- Cartan–Karlhede algorithm
- Cheeger constant
- Christoffel symbols
- Riemannian circle
- Clifford bundle
- Clifford module bundle
- Collapsing manifold
- Geodesic manifold
- Conformal map
- Conformally flat manifold
- Conjugate points
- Constant curvature
- Constraint counting
- Contorsion tensor
- Cotton tensor
- Covariance and contravariance of vectors
- Covariant derivative
- Curvature invariant
- Curvature of Riemannian manifolds
- Curved space
- Cut locus (Riemannian manifold)
F
G
H
K
L
M
P
R
S
- Santaló's formula
- Sasakian manifold
- Scalar curvature
- Schouten tensor
- Schur's lemma (Riemannian geometry)
- Second covariant derivative
- Second fundamental form
- Sectional curvature
- Sharafutdinov's retraction
- Smooth coarea formula
- Space form
- Spectral geometry
- Sphere theorem
- Spherical 3-manifold
- Spinor bundle
- Sub-Riemannian manifold
- Symmetric space
- Systolic freedom