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The following are the current most viewed articles on Wikipedia within Wikipedia's Riemannian geometry category. Think of it as a What's Hot list for Riemannian geometry. More info »

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Rank Topic Wikipedia views
1 Curvature 1,347 Sparkline of topic views for 2 weeks
2 Geodesic 966 Sparkline of topic views for 2 weeks
3 Conformal map 550 Sparkline of topic views for 2 weeks
4 Riemannian geometry 550 Sparkline of topic views for 2 weeks
5 Einstein notation 525 Sparkline of topic views for 2 weeks
6 Metric tensor 444 Sparkline of topic views for 2 weeks
7 Riemannian manifold 392 Sparkline of topic views for 2 weeks
8 Covariance and contravariance of vectors 343 Sparkline of topic views for 2 weeks
9 Covariant derivative 312 Sparkline of topic views for 2 weeks
10 Ricci curvature 304 Sparkline of topic views for 2 weeks
11 Riemann curvature tensor 299 Sparkline of topic views for 2 weeks
12 Ricci flow 283 Sparkline of topic views for 2 weeks
13 Christoffel symbols 239 Sparkline of topic views for 2 weeks
14 Nash embedding theorem 201 Sparkline of topic views for 2 weeks
15 Hodge dual 166 Sparkline of topic views for 2 weeks
16 Riemannian circle 155 Sparkline of topic views for 2 weeks
17 Tortuosity 151 Sparkline of topic views for 2 weeks
18 Pseudo-Riemannian manifold 141 Sparkline of topic views for 2 weeks
19 Killing vector field 136 Sparkline of topic views for 2 weeks
20 Geometrization conjecture 133 Sparkline of topic views for 2 weeks
21 Parallel transport 131 Sparkline of topic views for 2 weeks
22 Kähler manifold 130 Sparkline of topic views for 2 weeks
23 Holonomy 128 Sparkline of topic views for 2 weeks
24 Levi-Civita connection 123 Sparkline of topic views for 2 weeks
25 De Sitter space 120 Sparkline of topic views for 2 weeks
26 Exponential map 116 Sparkline of topic views for 2 weeks
27 Filling area conjecture 109 Sparkline of topic views for 2 weeks
28 Second fundamental form 103 Sparkline of topic views for 2 weeks
29 Laplace–Beltrami operator 102 Sparkline of topic views for 2 weeks
30 Musical isomorphism 100 Sparkline of topic views for 2 weeks
31 Scalar curvature 99 Sparkline of topic views for 2 weeks
32 Curvature of Riemannian manifolds 94 Sparkline of topic views for 2 weeks
33 Theorema Egregium 92 Sparkline of topic views for 2 weeks
34 Soul theorem 91 Sparkline of topic views for 2 weeks
35 Lie bracket of vector fields 77 Sparkline of topic views for 2 weeks
36 Curved space 70 Sparkline of topic views for 2 weeks
37 Einstein manifold 66 Sparkline of topic views for 2 weeks
38 Symmetric space 65 Sparkline of topic views for 2 weeks
39 Weyl tensor 63 Sparkline of topic views for 2 weeks
40 Gauss map 61 Sparkline of topic views for 2 weeks
41 Poincaré metric 59 Sparkline of topic views for 2 weeks
42 Sectional curvature 55 Sparkline of topic views for 2 weeks
43 Line element 55 Sparkline of topic views for 2 weeks
44 Systolic geometry 53 Sparkline of topic views for 2 weeks
45 De Sitter invariant special relativity 51 Sparkline of topic views for 2 weeks
46 Normal coordinates 48 Sparkline of topic views for 2 weeks
47 Uniformization theorem 46 Sparkline of topic views for 2 weeks
48 Geometric flow 45 Sparkline of topic views for 2 weeks
49 Gauss–Codazzi equations 42 Sparkline of topic views for 2 weeks
50 Comparison theorem 41 Sparkline of topic views for 2 weeks
51 Spin structure 40 Sparkline of topic views for 2 weeks
52 Constant curvature 39 Sparkline of topic views for 2 weeks
53 Hermitian manifold 38 Sparkline of topic views for 2 weeks
54 Glossary of Riemannian and metric geometry 37 Sparkline of topic views for 2 weeks
55 Fundamental theorem of Riemannian geometry 36 Sparkline of topic views for 2 weeks
56 Gromov–Hausdorff convergence 35 Sparkline of topic views for 2 weeks
57 Geodesic curvature 35 Sparkline of topic views for 2 weeks
58 Yamabe flow 35 Sparkline of topic views for 2 weeks
59 Ricci-flat manifold 33 Sparkline of topic views for 2 weeks
60 Harmonic map 31 Sparkline of topic views for 2 weeks
61 Hermitian symmetric space 30 Sparkline of topic views for 2 weeks
62 Ricci decomposition 28 Sparkline of topic views for 2 weeks
63 Hyperkähler manifold 26 Sparkline of topic views for 2 weeks
64 2π theorem 26 Sparkline of topic views for 2 weeks
65 Cheeger constant 26 Sparkline of topic views for 2 weeks
66 Filling radius 25 Sparkline of topic views for 2 weeks
67 Unit tangent bundle 24 Sparkline of topic views for 2 weeks
68 Abel–Jacobi map 24 Sparkline of topic views for 2 weeks
69 Total curvature 23 Sparkline of topic views for 2 weeks
70 Systoles of surfaces 22 Sparkline of topic views for 2 weeks
71 Space form 21 Sparkline of topic views for 2 weeks
72 Pu's inequality 21 Sparkline of topic views for 2 weeks
73 Essential manifold 21 Sparkline of topic views for 2 weeks
74 Cheng's eigenvalue comparison theorem 21 Sparkline of topic views for 2 weeks
75 Metric connection 21 Sparkline of topic views for 2 weeks
76 Geodesics as Hamiltonian flows 21 Sparkline of topic views for 2 weeks
77 Gromov's compactness theorem (geometry) 21 Sparkline of topic views for 2 weeks
78 Spectral geometry 21 Sparkline of topic views for 2 weeks
79 Jacobi field 20 Sparkline of topic views for 2 weeks
80 Seifert-Weber space 20 Sparkline of topic views for 2 weeks
81 Geodesic deviation equation 20 Sparkline of topic views for 2 weeks
82 Curvature invariant 20 Sparkline of topic views for 2 weeks
83 Isometry (Riemannian geometry) 20 Sparkline of topic views for 2 weeks
84 G2 manifold 19 Sparkline of topic views for 2 weeks
85 Hopf–Rinow theorem 19 Sparkline of topic views for 2 weeks
86 Cotton tensor 19 Sparkline of topic views for 2 weeks
87 Bolza surface 19 Sparkline of topic views for 2 weeks
88 Cut locus (Riemannian manifold) 19 Sparkline of topic views for 2 weeks
89 Conjugate points 18 Sparkline of topic views for 2 weeks
90 Sasakian manifold 18 Sparkline of topic views for 2 weeks
91 Loewner's torus inequality 18 Sparkline of topic views for 2 weeks
92 Introduction to systolic geometry 18 Sparkline of topic views for 2 weeks
93 Proofs involving Christoffel symbols 17 Sparkline of topic views for 2 weeks
94 Gravitational instanton 17 Sparkline of topic views for 2 weeks
95 Kretschmann scalar 17 Sparkline of topic views for 2 weeks
96 Nuts and bolts (general relativity) 17 Sparkline of topic views for 2 weeks
97 Gromov's inequality for complex projective space 16 Sparkline of topic views for 2 weeks
98 Conformally flat manifold 16 Sparkline of topic views for 2 weeks
99 Gauss's lemma (Riemannian geometry) 16 Sparkline of topic views for 2 weeks
100 Calibrated geometry 16 Sparkline of topic views for 2 weeks
101 De Sitter–Schwarzschild 16 Sparkline of topic views for 2 weeks
102 Cartan–Hadamard theorem 15 Sparkline of topic views for 2 weeks
103 Geodesic convexity 15 Sparkline of topic views for 2 weeks
104 Spherical 3-manifold 14 Sparkline of topic views for 2 weeks
105 Ruppeiner geometry 14 Sparkline of topic views for 2 weeks
106 Flat manifold 14 Sparkline of topic views for 2 weeks
107 Calabi flow 13 Sparkline of topic views for 2 weeks
108 Sphere theorem 13 Sparkline of topic views for 2 weeks
109 Collapsing manifold 13 Sparkline of topic views for 2 weeks
110 Schouten tensor 12 Sparkline of topic views for 2 weeks
111 Fermi coordinates 12 Sparkline of topic views for 2 weeks
112 Vector flow 11 Sparkline of topic views for 2 weeks
113 Quaternion-Kähler manifold 11 Sparkline of topic views for 2 weeks
114 Geodesic manifold 11 Sparkline of topic views for 2 weeks
115 Quaternion-Kähler symmetric space 11 Sparkline of topic views for 2 weeks
116 Smooth coarea formula 11 Sparkline of topic views for 2 weeks
117 Isoparametric manifold 11 Sparkline of topic views for 2 weeks
118 Lichnerowicz formula 11 Sparkline of topic views for 2 weeks
119 Sharafutdinov's retraction 11 Sparkline of topic views for 2 weeks
120 Orthonormal frame 10 Sparkline of topic views for 2 weeks
121 Almost flat manifold 10 Sparkline of topic views for 2 weeks
122 Gromov's systolic inequality for essential manifolds 10 Sparkline of topic views for 2 weeks
123 Schur's lemma (from Riemannian geometry) 10 Sparkline of topic views for 2 weeks
124 Bishop–Gromov inequality 9 Sparkline of topic views for 2 weeks
125 Toponogov's theorem 9 Sparkline of topic views for 2 weeks
126 Minimal volume 9 Sparkline of topic views for 2 weeks
127 Cartan–Karlhede algorithm 8 Sparkline of topic views for 2 weeks
128 Weyl–Schouten theorem 8 Sparkline of topic views for 2 weeks
129 Splitting theorem 7 Sparkline of topic views for 2 weeks
130 Bonnet theorem 7 Sparkline of topic views for 2 weeks
131 Synge's theorem 7 Sparkline of topic views for 2 weeks
132 Clifford bundle 7 Sparkline of topic views for 2 weeks
133 Berger's sphere 7 Sparkline of topic views for 2 weeks
134 Wiedersehen pair 7 Sparkline of topic views for 2 weeks
135 G2-structure 7 Sparkline of topic views for 2 weeks
136 Sub-Riemannian manifold 6 Sparkline of topic views for 2 weeks
137 Berger–Kazdan comparison theorem 6 Sparkline of topic views for 2 weeks
138 Harmonic coordinates 6 Sparkline of topic views for 2 weeks
139 Bryant surface 6 Sparkline of topic views for 2 weeks
140 Riemannian Penrose inequality 6 Sparkline of topic views for 2 weeks
141 Prescribed scalar curvature problem 6 Sparkline of topic views for 2 weeks
142 Constraint counting less than 5 views
143 Riemannian submersion less than 5 views
144 Berger's inequality for Einstein manifolds less than 5 views
145 First variation of area formula less than 5 views
146 Thurston elliptization conjecture less than 5 views
147 Myers's theorem less than 5 views
148 Riemannian submanifold less than 5 views
149 Beltrami's theorem less than 5 views
150 Spin(7)-manifold less than 5 views
151 Formulas in Riemannian geometry less than 5 views
152 Prescribed Ricci curvature problem less than 5 views
153 Weakly symmetric space less than 5 views
154 Hitchin–Thorpe inequality less than 5 views
155 Recurrent tensor less than 5 views
156 Calculus of moving surfaces less than 5 views

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Encyclopedia

From Wikipedia, the free encyclopedia

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 only the following subcategory.

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Pages in category "Riemannian geometry"

The following 157 pages are in this category, out of 157 total. This list may not reflect recent changes (learn more).

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