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Nomizu K. — Lie Groups and Differential Geometry
Nomizu K. — Lie Groups and Differential Geometry

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Название: Lie Groups and Differential Geometry

Автор: Nomizu K.

Аннотация:

This book is based on the manuscripts for a course on the theory of connections which I gave at Nagoya University in the winter of 1955, and is presented here as an introduction to ipodern differential geometry.
I wish to express my sincere gratitude to Professors Y. Kawada and K. Yano who have kindly suggested me to rearrange the lecture notes as a book for publication. It is my pleasant duty to acknowledge many helpful suggestions which Mr. N. Ivvahori has made for the improvement of the final redaction. My thanks go also to Mr. H. Ozeki who has kindly helped me by frequent discussions on the content and rendered a lot of service in proofreading.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 1st edition

Год издания: 1956

Количество страниц: 80

Добавлена в каталог: 29.08.2009

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
1-parameter group of differentiable transformations      5
Additional structure equation      51
Adjoint representation      15
Affine bundle      46
Affine connection in the generalized sense      73
Affine connection, associated to a linear connection      74
Affine transformation      66
Associated fiber bundle      21
Automorphism of a connection      37
Basic vector field      49
Bianchi's identity      62
Bundle of frames      23
Canonical parameter      63
Complete linear connection      64
Complete vector field      7
Completely parallelisable      2
Components of linear connection      56
Connection form      26
Connection in a principal fiber bundle      25
Connection in an associated fiber bundle      43
Covariant derivative      52
Covariant differential of a differential form      34
Covariant differential of a tensor field      55
Curvature form      34
Curvature tensor field      59
Differentiable homotopy      31 33
Differentiable transformation      3
Differentiate principal fiber bundle      17
distribution      3
Effective      16
Flat      41
Fundamental vector field      20
Geodesic      63
Holonomy algebra      39
Holonomy group      31 74
Holonomy theorem      39
Homogeneous part      46 75
Homomorphism of bundle      20
Homomorphism of connections      35
Horizontal curve      27
Horizontal subspace (component, vector field)      25
Infinitesimal affine transformation      67
Injection      20
Integral manifold      4
Jacobi's identity      4
Killing vector field      67
Lie subgroup      15
Lie transformation group      16
Lift of a curve      27
Lift of a vector field      26
Linear connection      49
Local 1-parameter group of local transformations      5
Locally flat      41
Non-homogeneous holonomy group      74
Normal coordinates      65
Normal neighborhood      65
Parallel displacement      31
Reduced bundle      21
Reducible, connection to      37
Reducible, structural group to      20
Reduction Theorem      37
Reference point      32
Restricted holonomy group      32
Riemannian connection      76
Riemannian metric      13
Structure equation      34
symmetric      77
Tensor fields of type (s,r)      13
Torsion form      51
Torsion tensor field      59
Transition functions      18
Translation part      46 75
Type ad(G)      34
Vertical component (vector field)      25
Without fixed point      16
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