相關商品
商品簡介
目次
商品簡介
This book provides the necessary foundation for students interested in any of the diverse areas of mathematics which require the notion of a differentiable manifold. It is designed as a beginning graduate-level textbook and presumes a good undergraduate training in algebra and analysis plus some knowledge of point set topology, covering spaces, and the fundamental group. It is also intended for use as a reference book since it includes a number of items which are difficult to ferret out of the literature, in particular, thecompleteand self-contained proofs of the fundamental theorems of Hodge and de Rham.
目次
1 MANIFOLDS
Preliminaries
Differentiable Manifolds
The Second Axiom of Countability
Tangent Vectors and Differentials
Submanifolds， Diffeomorphisms， and the Inverse Function Theorem
Implicit Function Theorems
Vector Fields
Distributions and the Frobenius Theorem
Exercises
2 TENSORS AND DIFFERENTIAL FORMS
Tensor and Exterior Algebras
Tensor Fields and Differential Forms
The Lie Derivative
Differential Ideals
Exercises
3 IE GROUPS
Lie Groups and Their Lie Algebras
Homomorphisms
Lie Subgroups
Coverings
Simply Connected Lie Groups
Exponential Map
Continuous Homomorphisms
Closed Subgroups
The Adjoint Representation
Automorphisms and Derivations of Bilinear Operations and Forms
Homgeneous Manifolds
Exercises
4 INTEGRATION ON MANIFOLDS
5 SHEAVES,COHOMOLGY,AND THE DE RHAM THEOREM
6 THE HODGE THEOREM
BIBLIOGRAPHY
SUPPLEMENT TO BIBLIOGRAPHY
INDEX OF NOTATION
INDEX
Preliminaries
Differentiable Manifolds
The Second Axiom of Countability
Tangent Vectors and Differentials
Submanifolds， Diffeomorphisms， and the Inverse Function Theorem
Implicit Function Theorems
Vector Fields
Distributions and the Frobenius Theorem
Exercises
2 TENSORS AND DIFFERENTIAL FORMS
Tensor and Exterior Algebras
Tensor Fields and Differential Forms
The Lie Derivative
Differential Ideals
Exercises
3 IE GROUPS
Lie Groups and Their Lie Algebras
Homomorphisms
Lie Subgroups
Coverings
Simply Connected Lie Groups
Exponential Map
Continuous Homomorphisms
Closed Subgroups
The Adjoint Representation
Automorphisms and Derivations of Bilinear Operations and Forms
Homgeneous Manifolds
Exercises
4 INTEGRATION ON MANIFOLDS
5 SHEAVES,COHOMOLGY,AND THE DE RHAM THEOREM
6 THE HODGE THEOREM
BIBLIOGRAPHY
SUPPLEMENT TO BIBLIOGRAPHY
INDEX OF NOTATION
INDEX
您曾經瀏覽過的商品
購物須知
大陸出版品因裝訂品質及貨運條件與台灣出版品落差甚大，除封面破損、內頁脫落等較嚴重的狀態，其餘商品將正常出貨。
特別提醒：部分書籍附贈之內容(如音頻mp3或影片dvd等)已無實體光碟提供，需以QR CODE 連結至當地網站註冊“並通過驗證程序”，方可下載使用。
無現貨庫存之簡體書，將向海外調貨：
海外有庫存之書籍，等候約45個工作天;
海外無庫存之書籍，平均作業時間約60個工作天，然不保證確定可調到貨，尚請見諒。
為了保護您的權益，「三民網路書店」提供會員七日商品鑑賞期(收到商品為起始日)。
若要辦理退貨，請在商品鑑賞期內寄回，且商品必須是全新狀態與完整包裝(商品、附件、發票、隨貨贈品等)否則恕不接受退貨。