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Thomas T.Y. — Concepts from Tensor Analysis and Differential Geometry
Thomas T.Y. — Concepts from Tensor Analysis and Differential Geometry

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Название: Concepts from Tensor Analysis and Differential Geometry

Автор: Thomas T.Y.

Аннотация:

In the following pages we have given an introductory account of the subject of tensor analysis and differential geometry. It is hoped that this volume will be suitable for a one-semester course at the graduate level, for students of pure mathematics as well as for tltose students whose primary interest is in the study of certain aspects of applied mathematics including the theory of relativity, fluid mechanics, elasticity, and plasticity theory.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1961

Количество страниц: 122

Добавлена в каталог: 08.07.2013

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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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