A first course in differential geometry
A first course in differential geometry
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DOI：
10.2307/3615543
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发表时间：
1981
期刊：
影响因子：
10.1
通讯作者：
C. Hsiung
中科院分区：
文献类型：
--
作者：
C. Hsiung
这本书的目的是介绍微分几何，以开始研究生以及先进的本科生。在过去的几十年里，微分几何和其他数学分支一起得到了很大的发展。在这本书中，我们将只研究传统的主题：即三维欧几里得空间E3中的曲线和曲面。然而，与大多数关于该主题的经典书籍不同，本书更多地关注局部和全局属性之间的关系，而不仅仅是局部属性。虽然我们在E3中将注意力限制在曲线和面上，但本书中大多数曲线和面的全局定理都可以扩展到更高维度的空间，或者更一般的曲线和面，或者两者兼而有之。并给出了几何解释和解析表达式。这使学生能够利用几何直觉，这是学习几何和相关问题的宝贵工具。
This book is designed to introduce differential geometry to beginning graduate students as well as to advanced undergraduate students. In the last couple of decades, differential geometry, along with other branches of mathematics, has been greatly developed. In this book we will study only the traditional topics: namely, curves and surfaces in a three-dimensional Euclidean space E3. Unlike most classical books on the subject, however, more attention is paid here to the relationships between local and global properties, as opposed to local properties only. Although we restrict our attention to curves and surfaces in E3, most global theorems for curves and surfaces in this book can be extended to higher dimensional spaces, to more general curves and surfaces, or to both. Moreover, geometric interpretations are given along with analytic expressions. This enables students to make use of geometric intuition, which is a precious tool for studying geometry and related problems.