Category:Riemannian geometry
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Here is a list of articles in the Riemannian geometry category of the Computing portal that unifies foundations of mathematics and computations using computers.
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 6 subcategories, out of 6 total.
C
G
S
Pages in category "Riemannian geometry"
The following 129 pages are in this category, out of 129 total.
- Riemannian geometry (computing)
*
- Glossary of Riemannian and metric geometry (computing)
- Proofs involving covariant derivatives (computing)
A
- Abel–Jacobi map (computing)
- Almost flat manifold (computing)
B
- Berger's sphere (computing)
- Biharmonic map (computing)
- Bishop–Gromov inequality (computing)
- Edmond Bonan (biography)
- Bryant surface (computing)
C
- Calculus of moving surfaces (computing)
- Calibrated geometry (computing)
- Cartan–Ambrose–Hicks theorem (computing)
- Cartan–Karlhede algorithm (physics)
- Cartan–Hadamard conjecture (computing)
- Cheeger constant (computing)
- Christoffel symbols (computing)
- Clifford bundle (computing)
- Clifford module bundle (computing)
- Collapsing manifold (computing)
- Geodesic manifold (computing)
- Conformal map (computing)
- Conformally flat manifold (computing)
- Conjugate points (computing)
- Constant curvature (computing)
- Constraint counting (computing)
- Contorsion tensor (computing)
- Cotton tensor (computing)
- Covariance and contravariance of vectors (computing)
- Covariant derivative (computing)
- Curvature invariant (computing)
- Curved space (computing)
- Cut locus (Riemannian manifold) (computing)
D
- De Sitter invariant special relativity (physics)
- De Sitter–Schwarzschild metric (computing)
E
- Einstein notation (computing)
- Essential manifold (computing)
- Exponential map (Riemannian geometry) (computing)
F
- Fermi coordinates (computing)
- Filling area conjecture (computing)
- Filling radius (computing)
- First variation of area formula (computing)
- Flat convergence (computing)
- List of formulas in Riemannian geometry (computing)
G
- G2 manifold (computing)
- G2-structure (computing)
- Gauss map (computing)
- Gauss–Codazzi equations (computing)
- Geodesic deviation (computing)
- Geometrization conjecture (computing)
- Great circle (computing)
- Gromov's inequality for complex projective space (computing)
- Gromov's systolic inequality for essential manifolds (computing)
- Gromov–Hausdorff convergence (computing)
H
- Harmonic coordinates (computing)
- Harmonic map (computing)
- Harmonic morphism (computing)
- Hermitian connection (computing)
- Hermitian manifold (computing)
- Hermitian symmetric space (computing)
- Hodge star operator (computing)
I
- Intrinsic flat distance (computing)
- Isometry (computing)
- Isometry (Riemannian geometry) (computing)
- Isoparametric function (computing)
- Isoparametric manifold (computing)
J
- Jacobi field (computing)
K
- Killing spinor (computing)
- Killing tensor (computing)
- Killing vector field (computing)
- Kosmann lift (computing)
- Kretschmann scalar (computing)
L
- Laplace–Beltrami operator (computing)
- Levi-Civita connection (computing)
- Lichnerowicz conjecture (computing)
- Lichnerowicz formula (computing)
- Lie bracket of vector fields (computing)
- Line element (computing)
- Loewner's torus inequality (computing)
M
- Macbeath surface (computing)
- Metric connection (computing)
- Metric Structures for Riemannian and Non-Riemannian Spaces (computing)
- Metric tensor (physics)
- Minimal volume (computing)
- Musical isomorphism (computing)
N
- Normal coordinates (computing)
O
- Orthonormal frame (computing)
P
- Parallel transport (computing)
- Poincaré metric (computing)
- Prescribed Ricci curvature problem (computing)
- Prescribed scalar curvature problem (computing)
- Pu's inequality (computing)
Q
- Quaternion-Kähler manifold (computing)
- Quaternion-Kähler symmetric space (computing)
R
- Rayleigh–Faber–Krahn inequality (computing)
- Recurrent tensor (computing)
- Ricci curvature (computing)
- Ricci decomposition (computing)
- Ricci soliton (computing)
- Riemann curvature tensor (computing)
- Riemannian circle (computing)
- Riemannian Penrose inequality (computing)
- Riemannian submersion (computing)
- Ruppeiner geometry (computing)
S
- Santaló's formula (computing)
- Sasakian manifold (computing)
- Schouten tensor (computing)
- Second covariant derivative (computing)
- Second fundamental form (computing)
- Sectional curvature (computing)
- Seifert–Weber space (computing)
- Sharafutdinov's retraction (computing)
- Smooth coarea formula (computing)
- Space form (computing)
- Spectral geometry (computing)
- Sphere theorem (computing)
- Spherical 3-manifold (computing)
- Spinor bundle (computing)
- Spinor field (physics)
- Symmetric space (computing)
- Systolic freedom (computing)
T
- Theorema Egregium (computing)
- Thurston elliptization conjecture (computing)
- Tortuosity (computing)
U
- Unit tangent bundle (computing)
W
- Weakly symmetric space (computing)
- Weyl tensor (computing)
- Wiedersehen pair (computing)
Y
- Yamabe problem (computing)