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Klingenberg W. — A Course in Differential Geometry (Graduate Texts in Mathematics)
Klingenberg W. — A Course in Differential Geometry (Graduate Texts in Mathematics)

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Название: A Course in Differential Geometry (Graduate Texts in Mathematics)

Автор: Klingenberg W.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1978

Количество страниц: 188

Добавлена в каталог: 07.08.2014

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
1-1 map      6
1-forms      111 113 114
2-form      111 113 114
Adjoint transpose of matrix      132
Alexandrov comparison theorem      162
Alexandrov, A.D.      162 168
Angle between vectors      76
Anosov, D.V.      164
Antipodal map      111
Area element      70 115
Asymptotic directions      53 54
Asymptotic lines      54
Atlas      105 124
Average curvature      31
Barner, M.      30
Base point of tangent vector      96
Berger, M.      120 164 168
Bernstein's theorem      70 71
Besse, A.      164
Bilinear forms      35 111
Bishop, R.      149 153 168
Blaschke, W.      29 30 129 135 164 167
Bonneson, T.      31
Bonnet, O.      139 152
Buchner, M.      165 166
Canal surface      67 68
Canonical projection      5
Catenoid      70
Cauchy — Riemann equations      121
Caustic surface      67 68
Change of coordinates for curves      8
Change of coordinates for surfaces      34
Charts on a manifold      105 123
Chern, S.S.      29 31 68 70 130 167 168
Christoffel symbols      61 74 91
Circle in the plane      17
Circle of hyperbolic geometry      30
Circle, geodesic      99 100
Clairaut's theorem      87 88 122
Closed curve      21
Closed geodesics      156
Closed set      2
Codazzi — Mainardi equation      62
Cohn-Vossen, S.      135 166 167
Comparison theorems      151 162
Completeness      146
Cone      57
Confocal surfaces      55 56
Conformal coordinates      120
Conformal surfaces      93
Congruence      2
Conjugacy class      158
Conjugate harmonic function      120
Conjugate point      148
Constant curvature surfaces      83—88 137
Constant Gauss curvature      66 93
Constant width curve      30
Continuous map      2
Continuously differentiable map      4
Contractible space      158
Convex curves      27—29
Convex surfaces      129
Coordinate charts      105 123
Coordinate invariance of covariant differentiation      91
Coordinate invariance of curvature tensor      92
Coordinate invariance of energy      91
Coordinate invariance of Frenet frame      91
Coordinate invariance of Gauss curvature      92
Coordinate systems      105 123
Coordinate vector field      34
Coordinates, asymptotic      53
Coordinates, change      8 34 74 90 113
Coordinates, conformal      120
Coordinates, Fermi      81
Coordinates, geodesic orthogonal      80—82
Coordinates, geodesic polar      99—101
Coordinates, isothermal      120
Coordinates, orthogonal      77
Coordinates, principal curvature      53
Coordinates, Riemann normal      99
Corners of a curve      27—29
Courant, R.      71
Covariant derivative      74 75 91
Covariant differential      76 91
Covering projection      158
Covering space      158
Crittenden, R.      149 153 168
Cross product      4
Curvature of a curve      13 15 17 18
Curvature tensor      63 91
Curvature, average      31
Curvature, constant      83—88 137
Curvature, constant Gauss      66 93
Curvature, Gauss      30 47 56 64 91
Curvature, geodesic      30 47 54 64 91
Curvature, mean      47
Curvature, normal      44
Curvature, principal      45—49
Curve in Euclidean space      8
Curve on surfaces      43—45
Curve, closed      21
Curve, constant width      30
Curve, convex      27—29
Curve, differentiable      106
Curve, locally minimizing      100
Curve, periodic      21
Curve, piecewise smooth      21
Curve, pretzel      27
Curve, regular      8
Curve, simply closed      21
Curve, space      17—20
Curve, unit speed      9 43
Curve, vertex of      28
Cusp      9 10
Cut locus      165
Cylinder over a curve      57
Darboux, G.      87 88 121 164 167
Developable surfaces      57—61
Dieudonne, J.      1
Diffeomorphism      4
Differentiable atlas      105
Differentiable curve      106
Differentiable function in Euclidean space      3
Differentiable function on manifolds      106
Differentiable manifold      105
Differential      4 5 115
Differential forms      111—119
Direct sum      111
Directrix of a ruled surface      57
Distance between points in Euclidean space      2
Distance between points on manifolds      144
Distinguished basis      1
Distinguished Frenet frame      11
Divergence      76 91
Do Carmo, M.      93 167
Douglas, J.      71
Dual basis      111
Dual map      111
Dual space      111
Dubins, L.      31
Dupin, C.      55
Edwards, C.      1 46 125
Efimov, N.W.      135 137
Eigenvalues as principal curvatures      46
Ellipsoid      55 68 69
Elliptic paraboloid      50 51
Elliptic point      50 51
Elliptical helix      20
Embedded submanifold      124
Embedded surface      123 124
Embedding into field of geodesics      83
Energy      9 91 110
Equivalence of atlases      105
Equivalent sets with Riemannian metric      90
Euclidean space      1
Euler characteristic      141—143
Exponential map      96—99
Exterior angle      23
Farey, I.      31
Fenchel, W.      31
Fermi coordinates      81
Field of geodesics      83
First fundamental form      35—38 43 46 73
Flanders, H.      65 168
Four Vertex Theorem      28 30
Frenet equations      11—15
Frenet frame      10 11 78 91
Fundamental group      157
Fundamental theorem of surface theory      64—66
Gauss curvature      30 47 48 54 64 91 92
Gauss equations      62
Gauss frame      35
Gauss lemma      100
Gauss map      35 38
Gauss theorema egregium      64
Gauss Theorema Elegantissimum      141
Gauss unit normal field along f      35
Gauss — Bonnet theorem      138—144
Gauss's theorem      117 119
Gauss, C.F.      29 64
General linear group      127
Generalized cylinder      61
Generated surface      42
Generator of ruled surface      57
Genus of surface      142
Geodesic circles      99 100
Geodesic completeness      60 154
Geodesic curvature      30 47 48 54 64 91
Geodesic orthogonal coordinates      80—82
Geodesic polar coordinates      99—101
Geodesics      78—83 91 95 101
Geodesics on sphere      79
Gluck, H.      30 166
Gradient      119
Graph      127
Green's formulae      120
Green, L.      164
Gromoll, D.      149 152 153 166 168
Grotemeyer, K.      135
Group of transformations      93
Gulliver, R.      72
Hadamard's characterization of ovaloids      130
Hadamard, J.      130 156
Harmonic functions      120
Hartman, P.      61
Heintze, E.      68
Heinz, E.      72
Helicoid      42
Helix      9 10
Herglotz integral formula      134
Herglotz, G.      29 30 134 135
Hilbert's nonexistence theorem      93
Hilbert, D.      68 93 167
Hildebrandt, S.      71 72
Homotopic curves      154
Hopf — Rinow theorem      146
Hopf, E.      164 165
Hopf, H.      24 68 93 130 146 167
Horn, R.      32
Hourglass surface      152
Hurewicz, W.      14 97
Hyperbolic paraboloid      50 51
Hyperbolic plane      92
Hyperbolic point      50 51
Hyperboloid      55
Hypersphere      126
Induced quadratic form      36
Inflection point of planar curve      16
Injective map      6
Injectivity radius      154
Inner product      1 36 73 109 124
Integrability conditions      62
Integral of 1-form      117
Integral of 2-form      118
Integral of differential equation      52
Interior of a set      2
Interior product      115
Intrinsic properties      73
Invariance of asymptotic directions      53
Invariance of curvature tensor      63 91 92
Invariance of energy integral      91
Invariance of first fundamental form      37
Invariance of Frenet equations      12 91
Invariance of second fundamental form      39
Inverse function theorem      6
Isometric surfaces      83 84
Isometry      83
Isometry of Euclidean space      2
Isoperimetric inequality      31
Isothermal coordinates      120
Isotropy subgroups      93
ith curvature of c      13
Jacobi fields      102—105 148
Jacobi, C.G.F.      143 164
Jacobian matrix      5
John, F.      52
Jordan curve theorem      31
k-times continuously differentiable      4
Karcher, H.      165
Kernel      6
Klingenberg, W.      72 149 152—154 163 168
Knotted curve      31
Kobayashi, S.      149 152 153 160 164 165 169
Laplace — Beltrami operator      120
Lefschetz, S.      138
Length of curve      9 91 110
Length of curve on surface      43
Length of vector      1
Lewy, H.      162
Lichtenstein, L.      120
Lie groups      98 127
Liebmann, H.      137
Line element      43 93
Line of curvature      53 55
Linear functional      111
Liouville line element      87 121
Liouville's theorem      122
Local diffeomorphism      6
Local linearization of differentiable map      6
Local surface with Riemannian metric      90
Locally minimizing curve      100 101
Lusternik, L.A.      163
Manifolds      89 105—111
Manifolds with Riemannian metric      109
Massey, W.      61 138 143 157
Matrix groups      127
Matrix representation of bilinear forms      36
Mean curvature      47
Meridians      87
Metric      144
Meusnier's theorem      43 44
Meyer, W.      149 152 153 166 168
Milnor, J.      31
Minimal surfaces      70—72 121
Minimizing curve      100 101
Minkowski integral formula      136
Minkowski, H.      136
Moving frame along c      10
Myers, S.      165
Nirenberg, L.      61 162 168
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