| 书目名称 | Differential Geometry of Curves and Surfaces |
| 编辑 | Shoshichi Kobayashi |
| 视频video | |
| 概述 | Is the long-awaited English translation of Kobayashi’s classic on differential geometry, acclaimed in Japan as an excellent undergraduate text.Focuses on curves and surfaces in 3-dimensional Euclidean |
| 丛书名称 | Springer Undergraduate Mathematics Series |
| 图书封面 |  |
| 描述 | .This book is a posthumous publication of a classic by Prof. Shoshichi Kobayashi, who taught at U.C. Berkeley for 50 years, recently translated by Eriko Shinozaki Nagumo and Makiko Sumi Tanaka. ..There are five chapters: 1. Plane Curves and Space Curves; 2. Local Theory of Surfaces in Space; 3. Geometry of Surfaces; 4. Gauss–Bonnet Theorem; and 5. Minimal Surfaces. ..Chapter 1 discusses local and global properties of planar curves and curves in space. Chapter 2 deals with local properties of surfaces in 3-dimensional Euclidean space. Two types of curvatures — the Gaussian curvature .K. and the mean curvature .H. —are introduced. The method of the moving frames, a standard technique in differential geometry, is introduced in the context of a surface in 3-dimensional Euclidean space. In Chapter 3, the Riemannian metric on a surface is introduced and properties determined only by the first fundamental form are discussed. The concept of a geodesic introduced in Chapter 2 is extensively discussed, and several examples of geodesics are presented with illustrations. Chapter 4 starts with a simple and elegant proof of Stokes’ theorem for a domain. Then the Gauss–Bonnet. .theorem, the ma |
| 出版日期 | Textbook 2019 |
| 关键词 | curves; surfaces; curvature; Riemannian metric; Gauss--Bonnet‘s theorem; minimal surfaces |
| 版次 | 1 |
| doi | https://doi.org/10.1007/978-981-15-1739-6 |
| isbn_softcover | 978-981-15-1738-9 |
| isbn_ebook | 978-981-15-1739-6Series ISSN 1615-2085 Series E-ISSN 2197-4144 |
| issn_series | 1615-2085 |
| copyright | Springer Nature Singapore Pte Ltd. 2019 |
发表于 2025-3-21 17:46:26
