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Lectures On Differential Geometry
◆World Scientific セール開催中！：2025年7月27日(日)ご注文分まで
※上記表示の販売価格は割引適用後の価格です 出版済み 3-5週間でお届けいたします。 Author: Fernandes, Rui Loja (University Of Illinois Urbana-champaign, Usa) Publisher: World Scientific ISBN: 9789811252648 Cover: HARDCOVER Date: 2024年09月 こちらの商品は学校・法人様向け（機関契約）のオンラインブック版がございます。 オンラインブックの価格、納期につきましては弊社営業員または当ECサイトよりお問い合わせください。  DESCRIPTION This book presents a concise introduction to differential geometry. It is aimed at advanced undergraduate students and first year graduate students who wish to have a basic solid knowledge of the subject, and it can serve as a starting point for more advanced reading. The book is organized into lectures, so it can easily be used as a textbook for a beginning graduate-level course in differential geometry. TABLE OF CONTENTS Basic Concepts: Manifolds as Subsets of Euclidean Space Abstract Manifolds Manifolds with Boundary Partitions of Unity The Tangent Space The Differential Immersions, Submersions, and Submanifolds Embeddings and Whitney's Theorem Foliations Quotients Lie Theory: Vector Fields and Flows Lie Bracket and Lie Derivative Distributions and the Frobenius Theorem Lie Groups and Lie Algebras Integrations of Lie Algebras The Exponential Map Groups of Transformations Differential Forms: Differential Forms and Tensor Fields Volume Forms and Orientation Cartan Calculus Integration on Manifolds de Rham Cohomology The de Rham Theorem Homotopy Invariance and Mayer-Vietoris Sequence Computations in Cohomology and Applications The Degree and the Index Fiber Bundles: Vector Bundles The Thom Class and the Euler Class Pullbacks of Vector Bundles The Classification of Vector Bundles Connections and Parallel Transport Curvature and Holonomy The Chern-Weil Homomorphism Characteristic Classes Fiber Bundles Principal Fiber Bundles
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