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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 |
Nitsche, J.C.C. 70 71 121
Nomizu, K. 152 169
Non-orientable surfaces 111
Nondegenerate quadratic form 112
Norm 1
Normal coordinates 99
Normal curvature 44
Normal form of surface 49—53
Normal local representation of space curve 18
Normal plane 19
Normal section 44
Normal vector field 34
One parameter group of isometries 41
Onto map 6
Open set 6
Open surfaces in the large 166
Orbit 42
Orientable surfaces 110 128
Orientation 110
Orientation preserving change of variables 8 34
Orientation preserving motion 2
Orthogonal component of isometry 2
Orthogonal coordinates 77
Orthogonal group 127
Orthogonal motion 2
Orthogonal transformation 2
Osculating circle 45
Osculating cone 58 77 78
Osculating developable 58 85
Osculating plane 19
Osserman, R. 31 71
Ovaloids 129—137
Parabolic cylinder 50 51
Parabolic point 50 51
Parallel circles 87
Parallel translation 76—78
Parallel vector field 76 77 85
Parameter transformation of a curve 8
Parameterization by arc length 9
Parameterized surface patch 33
Periodic curve 21
Piecewise smooth curve 21
Planar point 49 50
Planar surface 49
Plane curves 15—17
Plateau problem 71 72
Pogorelov, A. 61 162 163
Poincare half plane 92 94 95
Poincare, H. 165
Polar coordinates 99 100
Polygon 116
Polygonal decomposition of manifold 118
Positive definite quadratic form 35 133
Positively equivalent sets with Riemannian metric 90
Positively oriented basis 11
Positively oriented manifold 90 110
Pre-geodesic 79
Preissmann, L. 163 164
Pretzel curve 27
Prime geodesics 156
Principal curvature 45—49
Principal curvature coordinates 53
Principal directions 45 46
Projective plane 107
Pseudosphere 67 86 93
Quadratic form 35 112 133
Radius of injectivity 145
Rado, T. 71
Realization of surface with Riemannian metric 93
Rectifying plane 19
Reflection 2
Regular curve 8
Regular surface 33
Rembs, E. 135
Representation of tangent space 108
Riemann normal coordinates 99
Riemannian manifold 89
Riemannian metric 30 90 109 110 124
Rigidity of ovaloids 136
Rinow, W. 146
Rodriguez 46
Rotation 2
Rotation number 21—23
Ruled surfaces 56 57
Scalar product 1
Schnirelmann, L. 163
| Schwarz inequality 1
Second fundamental form 38 39 43 46
Second order surfaces 127
Seifert, H. 138 164
simplex 116
Simply closed curve 21
Singer, D. 166
Singer, I.M. 158 168
Singular polygon 116
Singular simplex 116
Skew symmetric bilinear form 112
Space curves 17—20
Special linear group 94
Special orthogonal group 127
Sphere 40 66 77 86 106 126 137
Spherical surface 49
Spivak, M. 1 51 65 127 168
Spruck, J. 72
Star shaped 22
Steiner, J. 31
Stoker, J. 69
Straight line 10 16 17
Strubecker, K. 67 70 168
Sturm comparison theorem 150
Sturm, J.C.F. 150
surface 33 105 123
Surface generated by one parameter group of isometries 41
Surface of genus g 142
Surface patch 33
Surface with Riemannian metric 90
Surfaces of revolution 41 66 70 87 88
Surjective map 6
Symmetric bilinear form 35
Symmetry 2
Tangent bundle 95 96 109
Tangent bundle of open set 5
Tangent field along c 8
Tangent space 96 108
Tangent space of a surface 33
Tangent space of Euclidean space 5
Tangent vector 95 96 108
Tangent vector field of c 8
Tangential developable surface 47
Tangential mapping of curve 22
Tangential vector field 34 74
Theorema egregium 64
Theorema Elegantissimum 141
Third fundamental form 39 48
Thorbergsson, G. 30
Thorpe, J. 158 168
Threlfall, W. 138 164
Topological atlas 105
Topological manifold 105
Torsion of space curve 17 18
Torus 40 126
Total curvature 31
Tractrix 67
Transformation groups 93
Transitive group action 93
Translation 2
Trefoil 27
Triangle inequality 1 144
Triangulation 141
Triply orthogonal family of surfaces 54
Twice continuously differentiable 4
Umbilic 49
Umlaufsatz 24
Unit normal field along f 35
Unit speed curve 9 43
Unparameterized curve 9
Unparameterized surface 34
Vector field 109
Vector field along c 8
Vector field along f 34
Vertex of a curve 28
Voss, K. 68
W-surface 68
Warner, F. 127 169
Wedge product 112
Weingarten map 39 53
Weingarten surface 68
Weinstein, A. 164
Weyl, H. 161 162
Wiedersehen pair 164
Wiedersehen surface 164
Zoll surfaces 164
Zoll, O. 164
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