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Morita S. — Geometry of differential forms
Morita S. — Geometry of differential forms

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Название: Geometry of differential forms

Автор: Morita S.


Since the times of Gauss, Riemann, and Poincaré, one of the principal goals of the study of manifolds has been to relate local analytic properties of a manifold with its global topological properties. Among the high points on this route are the Gauss-Bonnet formula, the de Rham complex, and the Hodge theorem; these results show, in particular, that the central tool in reaching the main goal of global analysis is the theory of differential forms.

The book by Morita is a comprehensive introduction to differential forms. It begins with a quick introduction to the notion of differentiable manifolds and then develops basic properties of differential forms as well as fundamental results concerning them, such as the de Rham and Frobenius theorems. The second half of the book is devoted to more advanced material, including Laplacians and harmonic forms on manifolds, the concepts of vector bundles and fiber bundles, and the theory of characteristic classes. Among the less traditional topics treated is a detailed description of the Chern-Weil theory.

The book can serve as a textbook for undergraduate students and for graduate students in geometry.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2001

Количество страниц: 321

Добавлена в каталог: 12.09.2007

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Предметный указатель
Section      172 233
Self-adjoint      155
Signature      166
Simplicial complex      97
Singular chain complex      100
Singular homology group      100
Singular homology theory      96
Singular k-chain      100
Singular k-simplex      100
Singular point of the vector field      42
SO (n)      23
Special orthogonal group      23
Stabilizer      50
Standard k-simplex      99
Stiefel — Whitney class      227
Stokes theorem      107
Stokes theorem on chains      109
Structure constant      91
Structure equation      188 265
Structure group      234
Subbundle      174
Submanifold      20
Submersion      34
Support      29 106
Symbol      162
Symplectic form      93
System of Pfaffian equations      88
Tangent bundle      170
Tangent frame bundle      240
Tangent space      6 30
Tangent vectors      7 30
Topological manifold      13
Topological space      3
Topologically invariant      100
Torsion tensor      203
Total Chern class      206
Total differential      59
Total Pontrjagin class      201
Total space      171 232
Transition function      171
Triangle inequality      3
Triangulation      97
Trivial bundle      232
Trivial connection      185
Trivialization      171
Unit sphere bundle      256
Unitary group      23
Universal covering manifold      51
Universal G-bundle      239
Upper half space      44
Vector bundle      171
Vector field      9 37
Vector space      6
Velocity vector      8
Vertical vector      259
Volume element      151
Volume form      139 151
Weil algebra      268
Weil homomorphism      275 278
Whitney formula      207—208
Whitney sum      176
Whitney's embedding theorem      10
Zero section      172
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