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| Авторизация |
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| Поиск по указателям |
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| Klingenberg W. — A Course in Differential Geometry (Graduate Texts in Mathematics) |
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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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