買這商品的人也買了...
商品描述
Intended for a one year course, this text serves as a single source, introducing readers to the important techniques and theorems, while also containing enough background on advanced topics to appeal to those students wishing to specialize in Riemannian geometry. This is one of the few Works to combine both the geometric parts of Riemannian geometry and the analytic aspects of the theory. The book will appeal to a readership that have a basic knowledge of standard manifold theory, including tensors, forms, and Lie groups.
Important revisions to the third edition include:
- a substantial addition of unique and enriching exercises scattered throughout the text;
- inclusion of an increased number of coordinate calculations of connection and curvature;
- addition of general formulas for curvature on Lie Groups and submersions;
- integration of variational calculus into the text allowing for an early treatment of the Sphere theorem using a proof by Berger;
- incorporation of several recent results about manifolds with positive curvature;
- presentation of a new simplifying approach to the Bochner technique for tensors with application to bound topological quantities with general lower curvature bounds.
From reviews of the first edition:
"The book can be highly recommended to all mathematicians who want to get a more profound idea about the most interesting achievements in Riemannian geometry. It is one of the few comprehensive sources of this type."
―Bernd Wegner, ZbMATH
商品描述(中文翻譯)
本書旨在用於一年的課程，作為單一來源，向讀者介紹重要的技術和定理，同時也包含足夠的高級主題背景，以吸引希望專攻黎曼幾何的學生。這是少數幾本結合黎曼幾何的幾何部分和理論的分析方面的著作之一。本書適合對標準流形理論有基本了解的讀者，包括張量、形式和李群。
第三版的重要修訂包括：
- 在文本中散佈大量獨特且豐富的練習題；
- 增加了連接和曲率的坐標計算數量；
- 增加了李群和潛射上的曲率的一般公式；
- 將變分法整合進文本中，允許對球面定理的早期處理，並使用Berger的證明；
- 融入了幾個有關正曲率流形的最新結果；
- 提出了一種新的簡化方法來處理張量的Bochner技術，並應用於具有一般下曲率界限的有界拓撲量。
來自第一版的評價：
「本書非常推薦給所有希望深入了解黎曼幾何中最有趣成就的數學家。它是這類綜合性來源中為數不多的幾本之一。」
―Bernd Wegner, ZbMATH
作者簡介
Peter Petersen is a Professor of Mathematics at UCLA. His current research is on various aspects of Riemannian geometry. Professor Petersen has authored two important textbooks for Springer: Riemannian Geometry in the GTM series and Linear Algebra in the UTM series.
作者簡介(中文翻譯)
彼得·彼得森（Peter Petersen）是加州大學洛杉磯分校（UCLA）的數學教授。他目前的研究專注於黎曼幾何的各個方面。彼得森教授為施普林格（Springer）撰寫了兩本重要的教科書：GTM 系列的《黎曼幾何》（Riemannian Geometry）和 UTM 系列的《線性代數》（Linear Algebra）。
