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| Thomas T.Y. — Concepts from Tensor Analysis and Differential Geometry |
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| Предметный указатель |
Absolute differentiation 46 84
Addition of tensors 10
Affine geometry 56
Affine geometry of paths 31
Affine normal tensors 50
Affinely connected space 30
Allowable coordinates 4
Allowable coordinates, transformations 5
Angle, definition of 23
Arithmetic space 1
Asymptotic lines 99
Binormal 72
Cartesian coordinates 55 58
Christoffel symbols 26
Codazzi equations 92
Congruent configurations 56
Contraction of tensors 11
Coordinate manifolds 5
Coordinate systems 1
Coordinate systems, allowable 3 5 17 21 75
Coordinate systems, Cartesian 55 58
Coordinate systems, curvilinear 75
Coordinate systems, normal 33
Coordinate systems, preferred 54 60
Coordinate systems, rectangular 55 62
Coordinate transformations 1
Coordinate transformations, affine 55
Coordinate transformations, allowable 5 17 21 75
Covariant differentiation 39 43 44 83
Curl of a vector 16 19
Curvature of a curve 71
Curvature tensor 51
Curvilinear coordinates 75
Developable surfaces 114
Differential invariants 48
Differential invariants, affine 50
Differential invariants, metric 48 50
Direction, definition of 23
Distance, definition of 17 57
Edge of regression 114
Enneper, equation of 100
Equivalent configurations 56
Euclidean 55 56
Euclidean metric 56 64
Euclidean metric of paths 31
Euclidean, normal 34
Euclidean, orthogonal 55 56
Euclidean, proper 3 56
Euclidean, regular 2
Euclidean, transformation 54—56
Extension of tensors 39 42 44 83
Extension of tensors, absolute 47 84
First fundamental form 77
Flat points 96
Frenet formulae 73
Frenet formulae for plane curves 74
Fundamental metric tensor 17
Gauss equations 92
Gauss equations, formulae 88
Gaussian curvature 90 100
Geodesic curvature 86
Geodesic curvature, curves 26
Geometry, affine 56
Gradient of a function 79
Group of the manifold 4
Groups, abstract 3
Groups, abstract, affine 55 56
Homogeneous tensors 65
| identities 51—53
Identities, complete sets of 53
Isotropic tensors 65—69
Kjonecker delta 2
Length of curves 22
Length of curves, vectors 22
Lines of curvature 98
Mean curvature 90
Metric differential invariants 48 50
Metric differential invariants, normal tensors 50
Minimal surfaces 114
Mixed tensors 9 81
Multiplication of tensors 10
Normal congruence 102
Normal congruence, curvature 94
Normal congruence, vectors 70 77
Normal coordinates 33
Normal coordinates, characterization of 36—38
Normal coordinates, transformations of 34
Oriented manifolds 3
Oriented manifolds, spaces 18 21 56
Oriented manifolds, surfaces 78
Orthogonal ennuples 101
Orthogonal ennuples, group 55
Orthogonal ennuples, transformations 55
Parallel displacement 47
Parallel displacement, surfaces 108—113
Paths 30
Plane, equation of 61
Plateau, problem of 115
Preferred systems 54 60
Principal curvatures 95
Principal curvatures, directions 95
Principal curvatures, normal vector 71
Rank of a tensor 10
Rectangular coordinates 55
Regular curve 22
Regular curve, surface 75
Regular curve, transformations 2
Relative tensor, definition of Riemann space 17
Relative tensor, locally flat 60
Relative tensor, oriented 18
Relative tensor, reducible 60
Rotation of a vector 16 19
Scalar, definition of 6
Scalar, product 8 20
Second fundamental form 88
Similar configurations 56
Simple manifolds 3
Skew-symmetric tensors 11 13—15 21 22
Space, affine 55
Space, affinely connected 30
Space, Euclidean 55
Space, Euclidean metric 55 57—64
Straight line, equations of 61
Surface and space tensors 81
Symmetric tensor, definition of 11
Tangent developable 114
Tangent vector 47 70
Tensor, absolute 12
Tensor, definition of 9
Tensor, relative 11
Torsion of a curve 72 74
Transformation groups 54—56
Umbilical point 97
Vector, definition of 7
Vector, product 16 19
Volume 25
Weingarten, formulae of 88
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