滑らかな多様体入門 Introduction to Smooth Manifolds (Graduate Texts in Mathematics .218) （2002. XVII, 628 S. 157 SW-Abb. 235 mm）

Lee, John M.

SPRINGER, BERLIN（2002発売）

• 製本 Hardcover:ハードカバー版／ページ数 628 p.
• 言語 ENG
• 商品コード 9780387954950

Full Description

Author has written several excellent "Springer" books. This book is a sequel to "Introduction to Topological Manifolds". It features careful and illuminating explanations, excellent diagrams and exemplary motivation. It includes short preliminary sections before each section explaining what is ahead and why.

Contents

Preface * Smooth Manifolds * Smooth Maps * Tangent Vectors * Vector Fields * Vector Bundles * The Cotangent Bundle * Submersions, Immersions, and Embeddings * Submanifolds * Lie Groups Actions * Embedding and Approximation Theorems * Tensors * Differential Forms * Orientations * Integration on Manifolds * De Rham Cohomology * The de Rham Theorem * Integral Curves and Flows * Lie Derivatives * Integral Manifolds and Foliations * Lie Groups and Their Lie Algebras * Appendix: Review of Prerequisites * References * Index