Global Differential Geometry Vol 1: Basic of Riemannnian Geometry (2nd edition)
Wu-Hsiung Huang
- PublishedOctober, 2021
- Binding精裝 / 26*19 / 328pages / 單色(黑) / 中文
- Publisher國立臺灣大學出版中心
- SeriesEducation－Textbooks
- ISBN978-986-350-511-2
- GPN1011001533
- Price NT$600
- Paper Books San Min Books / wunan / books.com.tw / National Books / iRead / eslite / TAAZE /
- EISBN(PDF)978-986-350-538-9
- Preview Google Books
Global Differential Geometry, a comprehensive three-volume set of thirty chapters, focuses on curved spaces. The volume one is largely based on the author's lecture notes at National Taiwan University. Starting from this very fundament, the volume two and three delve into professional research of global geometry. Additionally, the first and third volumes include three chapters respectively of "Preliminary Topics" and "Extended Topics," as an introduction and an advanced learning extension of differential geometry.
The volume one starts with the fundamentals of "Global Surface Theory," "Moving Frames," and "Differentiable Manifolds" in chapters A, B, and C of the "Preliminary Topics," introducing Riemannian geometry and exploring his higher-dimensional intrinsic geometry of "curved spaces." The book particularly emphasizes geometric intuition and preliminarily explores the global geometric properties of curved spaces through the "geodesic variational principle."
大域微分幾何引言
《大域微分幾何》三卷書二版序
校訂序
中文譯名說明
上卷 Riemann幾何基礎
前篇 基礎背景
章A 大域曲面論概要
章B 活動標架法初步及其應用
章C 可微流形的基礎概念
篇一 Riemann幾何的背景
第1章 切向量與Lie微分
第2章 Frobenius可積分定理
第3章 Riemann曲率的誕生
第4章 曲面論基本定理
篇二 測地線的變分
第5章 向量場的共變微分
第6章 Connection, metric與曲率
第7章 測地線的變分與Synge定理
第8章 變分學中的Direct Method
篇三 Jacobi場與大域幾何
第9章 Exponential map與最短測地線
第10章 Jacobi場
第11章 測地線的大域行為
第12章 Bonnet-Myers定理與Hadamard定理
附錄
Appendix A
全書參考文獻
全書索引