Hicks N. — Notes on differential geometry :: Электронная библиотека попечительского совета мехмата МГУ

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Hicks N. — Notes on differential geometry

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Название: Notes on differential geometry

Автор: Hicks N.

Аннотация:

The first three chapters of this book provide a short course on classical differential geometry and could be used at the junior level wih a little outside reading in linear algebra and advaced calculus.
The first six chapters can be used for a one-semester course in differential geometry at the senior-graduate level. The entire book can be covered in a full year course.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1965

Количество страниц: 181

Добавлена в каталог: 08.06.2005

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

Предметный указатель

Alternating tensor      50
Area      73 303
Asymptotic coordinates      136
Asymptotic vector      24 76
Atlas      2
Base field      13
Beltrami operators      139
Bianchi identities      72 95
Boundary map      98
Bounding curve      105
Bracket      3
Bundle of bases      17
Carlan structural equations      61
Cartan differential algebra      91
Catan formula (geodesic curvature)      107
Catenoid      49
Center surfaces      48
Chain      98
Characteristic classes      117
Characteristic forms      117
Characteristics      15
Closed distribution      123
Coardinate system (special)      13
Cochains      95
Codazzi — Mainardi equation      28 76 82 89
Cohomology group (differential)      117
complete      60 71 163
conformal      73
Congruent surface      120
Conjugate degree      157
Conjugate point      146
Conjugate vectors      24 76
Connexion      20 26 56 66
Connexion 1-forms      61 67
Connexion preserving map      60
Contraction      91
Convex neighborhood      134
Coordinate pair      2
Coordinate system      2
Cotangent bundle      56
Covariant differentiation      18 20 26 56 94
Critical point      157
Cuba      98
Curvature tensor      59
Curve      10
Curve (broken)      13
Developable surface      32
Diffeomorphism      9
Difference tensor      54
Differential of a map      9
Divergence      95
Dupin indicatrix      25
Euler characteristic      108
Excess      108
Exponential map      131
Exterior algebra      51
Exterior derivative      62 89
Exterior product      51
Extramal      149
Fermi coordinates      133
Fiber      17
First variation formula      148
Flat connexion      68
Flat point      24 76
Flat space      83
Forms      50
Framed      52
Frenet formulae      74
Fuindamental set      102
Function,       3
Fundamental 1-form      56
Fundamental forms      24
Fundamental n-chain      102
Gauass — Bonnet form      115
Gauss curvature      24
Gauss curvature equation      28 76 82 89
Gauss equation      25 75 82
Gauss map      22
General covariant derivative      94
General linear group GL(n, R)      2
Geodesic      19 27 57
Geodesic curvature      74 104 107
Geodesic flow field      132
Geodesic preserving map      60
Geodesic submanifold      158 174
Gradient      96
Grassman algebra      51
Grassman product      51
Helicoid      38
hessian      157
Holonomy      68
Homathetic      73
Homology      98
Hyperbolic space      83
Hypersurface      21
Imbedding      13
Immersion      13
Index (function)      157
Index (vector field)      111 115
Inner product      21
Integrable distribution      123

Integral curve      11
Integral manifold      123
Invariant polynomial      117
Involutive distribution      123
Isomelry      73
Isometric      73
IsothermaI coordinateas      135
Jacobi field      144
Jacobi identity      9
Jacobian map      9
Lagrange identity      152
Laplacian      96 139
Left invariant connexion      68
Left invariant fields      16
Length (curve)      69
Length (vector)      69
Lie algebra      16
Lie derivative      92
Lie group      5
Line of curvature      24 46
Manifold      2
Mean curvature      24
Metric      71
Metric preserving connexion      87
Metric tensor      21 69
Minimal surface      41 43 49 141
Normal (of a curve)      74
Normal coordinates      133
Normal curvature      76
Normal deformation      141
One parameter subgroup      16 93
One--parameter family of curves      144
Open set      3
Orientable      101
Orthogonal coordinates      136
Parallel hypersurface      35
Parallel translation      19 27 57
Parallelizable      14 68
Partition of unity      85
Poincare space      83
Pole      287
Principal coordinates      136
Principal curvature      24
Principal vector      24
Pseudo-rneiric      70
Ricci tensot, map and curvature      95 96
Riemann space      83
Riemann surface      140
Riemann — Christoffel curvature      72 95
Riemannian connexion      21 71
Riemannian curvature      73 155
Riemannian manifold      20
Riemannian metric      21
Rigidity      79
Rodrigues formula      25
Rotation group      68
Ruled surface      32
Scalar curvature      36
Second fundamental form      24
Second fundamental tensor      75
Second variation formula      148
Self-adjoint (symmetric) map      22
Semi-Riemannian manifold      21
Shuffle permutation      55
Simple closed curve      106
Skew-symmetric tensor      50
Slice      123
Special orthogonal group      68
Sphere map      99
Spherical space      83
Stokes map      99
Structural function      17
Subatlas      2
Submanifold      13 75
Support      98 103
Surface of revolution      45
Symmetric surfaces      120
Symmetric tensor      50
Tangent (of a curve)      30
Tangent bundle      16
Tangent space      6
Tensor algebra      51
Tensors      49
Torsion (of a curve)      74
Torsion tensor      59 78
Torus (flat)      16
Total curvature      24
Tractrix      49
Two parameter family of curves      158
Umbilic      24
Universal covering manifold      170
Universal tensors      54
Vector      5
Vector field      8
Vector field (on submanifold)      14
Vertical vector      17
Volume      103
Volume element      102
Wedge product      51
Weil homomorphism      117
Weingarten map      21 77 82 89
Weingarten surface      141

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