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Words: 3k
Articles: 136
Table of contents
3k
136
Immersion
Differential geometry
51
1
Isothermal coordinates
Immersion
21
Laplace-Beltrami operator
Differential geometry
18
Smooth surface
Differential geometry
24
Smooth manifold
Differential geometry
150
5
Abstract smooth surface
Smooth manifold
73
1
Smooth quotient by a free finite group action
Abstract smooth surface
46
Smooth map between manifolds
Smooth manifold
19
Orientable smooth manifold
Smooth manifold
37
1
Orientation-reversing diffeomorphism
Orientable smooth manifold
16
Riemannian metric
Differential geometry
18
Tangent vector
Differential geometry
85
3
Tangent space
Tangent vector
30
Unit tangent vector
Tangent vector
15
Velocity vector
Tangent vector
16
Normal vector
Differential geometry
19
1
Unit normal
Normal vector
8
Orientation of a surface
Differential geometry
44
1
Boundary orientation
Orientation of a surface
25
First fundamental form
Differential geometry
184
7
Local isometry
First fundamental form
113
4
Geodesic preservation by a local isometry
Local isometry
46
1
Geodesic-preserving homothety that is not a local isometry
Geodesic preservation by a local isometry
26
Riemannian isometry
Local isometry
18
Local isometry from a circular cone to the plane
Local isometry
25
Area element of a surface
First fundamental form
38
1
Vector area element
Area element of a surface
14
Gauss map
Differential geometry
417
16
Second fundamental form
Gauss map
397
15
Shape operator
Second fundamental form
91
3
Principal curvature
Shape operator
42
1
Umbilical point
Principal curvature
26
Euclidean invariance of the shape operator
Shape operator
30
Gaussian curvature
Second fundamental form
48
1
Gaussian curvature of a cone away from its vertex
Gaussian curvature
38
Mean curvature
Second fundamental form
57
2
Minimal surface
Mean curvature
16
Orientation reversal of surface curvature
Mean curvature
23
Fundamental forms of a graph surface
Second fundamental form
178
5
Gaussian curvature of a graph surface
Fundamental forms of a graph surface
7
Mean-curvature comparison at tangential contact
Fundamental forms of a graph surface
81
1
Gaussian curvature has no tangential-contact comparison principle
Mean-curvature comparison at tangential contact
43
Tangency to a plane along a curve forces zero Gaussian curvature
Fundamental forms of a graph surface
48
Minimal surface equation for a graph
Fundamental forms of a graph surface
25
Smooth curve
Differential geometry
46
2
Regular curve
Smooth curve
30
1
Arc-length parametrization
Regular curve
19
Curvature and torsion
Differential geometry
159
5
Curvature of a space curve
Curvature and torsion
60
1
Plane curve reconstructed from curvature
Curvature of a space curve
33
Total curvature
Curvature and torsion
45
Torsion of a space curve
Curvature and torsion
18
Planar curves have zero torsion
Curvature and torsion
21
Steiner symmetrization
Differential geometry
129
5
Cavalieri principle
Steiner symmetrization
14
Area preservation under Steiner symmetrization
Steiner symmetrization
16
Perimeter decrease under Steiner symmetrization
Steiner symmetrization
49
1
Equality case in the Steiner perimeter inequality
Perimeter decrease under Steiner symmetrization
22
Symmetrization rigidity for a perimeter minimizer
Steiner symmetrization
32
Frenet-Serret formulas
Differential geometry
202
7
Frenet frame
Frenet-Serret formulas
22
Euclidean motion of Euclidean three-space
Frenet-Serret formulas
47
1
Proper Euclidean motion of Euclidean three-space
Euclidean motion of Euclidean three-space
23
Circular helix
Frenet-Serret formulas
16
Pointwise Euclidean invariant of a curve
Frenet-Serret formulas
63
1
Pointwise Euclidean invariants need not depend only on current curvature and torsion
Pointwise Euclidean invariant of a curve
32
Curvature decomposition for a spherical curve
Frenet-Serret formulas
18
Geodesic curvature
Differential geometry
183
4
Transitive curve symmetry makes geodesic-curvature magnitude constant
Geodesic curvature
35
Isometric halves give zero total boundary geodesic curvature
Geodesic curvature
38
Homogeneous nongeodesic latitude
Geodesic curvature
28
Antipodally symmetric nongeodesic spherical curve
Geodesic curvature
39
Gauss-Bonnet theorem
Differential geometry
151
5
Area of a hyperbolic geodesic polygon
Gauss-Bonnet theorem
22
Spherical isoperimetric inequality
Gauss-Bonnet theorem
55
Gaussian curvature of a torus
Gauss-Bonnet theorem
20
Total Gaussian curvature
Gauss-Bonnet theorem
15
Intersection of closed geodesics on a positively curved sphere
Gauss-Bonnet theorem
35
Preimage theorem
Differential geometry
21
Theorema Egregium
Differential geometry
16
Riemannian geometry
Differential geometry
572
22
Riemannian surface
Riemannian geometry
19
Arc length
Riemannian geometry
11
Isometry
Riemannian geometry
14
Geodesic
Riemannian geometry
376
11
Geodesic triangle
Geodesic
23
Surface covariant derivative
Geodesic
36
Exponential map
Geodesic
170
4
Domain of the exponential map
Exponential map
72
1
Exponential map of the punctured plane
Domain of the exponential map
41
Geodesic polar coordinates
Exponential map
61
1
Gauss lemma
Geodesic polar coordinates
34
Complete geodesic
Geodesic
36
1
Hopf-Rinow theorem
Complete geodesic
20
Tangency invariance of an ambient-surface geodesic
Geodesic
79
1
Cylindrical-helix tangency construction
Tangency invariance of an ambient-surface geodesic
32
Energy of a curve
Riemannian geometry
14
Christoffel symbol
Riemannian geometry
10
Geodesic equation
Riemannian geometry
114
4
Ambient acceleration criterion for a surface geodesic
Geodesic equation
50
1
Constant speed of an affinely parametrized geodesic
Ambient acceleration criterion for a surface geodesic
24
Normal section of a surface
Geodesic equation
16
Affine parameter
Geodesic equation
33
Embedded surface parametrization
Differential geometry
13
Surface of revolution
Differential geometry
287
10
Catenoid
Surface of revolution
23
Constant strip-area density of a surface of revolution
Surface of revolution
52
Curvature-matching diffeomorphism between two surfaces of revolution
Surface of revolution
33
First fundamental form of an arc-length surface of revolution
Surface of revolution
113
4
Curvatures of an arc-length surface of revolution
First fundamental form of an arc-length surface of revolution
101
3
Constant Gaussian curvature surfaces of revolution
Curvatures of an arc-length surface of revolution
54
Gaussian curvature of a surface of revolution
Curvatures of an arc-length surface of revolution
33
1
Total Gaussian curvature of a surface-of-revolution strip
Gaussian curvature of a surface of revolution
19
Circular cylinder
Surface of revolution
21
Clairaut first integral for a surface of revolution
Surface of revolution
24
Helicoid
Differential geometry
20
Ruled surface
Differential geometry
130
4
One-sheet hyperboloid
Ruled surface
115
3
Plane-section geodesics of the unit one-sheet hyperboloid
One-sheet hyperboloid
37
Geodesic trapped in one half of the unit one-sheet hyperboloid
One-sheet hyperboloid
36
Isometry-invariant waist geodesic of the unit one-sheet hyperboloid
One-sheet hyperboloid
29
Flat cone
Differential geometry
43
2
Developing map
Flat cone
12
Isometry of a cone
Flat cone
17
Manifold chart
Differential geometry
41
1
No compact manifold has a single Euclidean chart
Manifold chart
22
Regular value
Differential geometry
63
2
Regular level set theorem
Regular value
24
Sard theorem
Regular value
24
Degree modulo two
Differential geometry
94
1
Exponential displacement map on a compact surface
Degree modulo two
36
Symplectic group
Differential geometry
38
1
Tangent space of the symplectic group
Symplectic group
20
Grassmannian as projection matrices
Differential geometry
57
2
Rank-one orthogonal projection
Grassmannian as projection matrices
20
Real projective plane
Grassmannian as projection matrices
21
Ancestors
(4)
Geometry and topology
Area of mathematics
Mathematics
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