Description: Differential Geometry of Curves and Surfaces Please note: this item is printed on demand and will take extra time before it can be dispatched to you (up to 20 working days). Author(s): Shoshichi Kobayashi, Eriko Shinozaki Nagumo, Makiko Sumi Tanaka Format: Paperback Publisher: Springer Verlag, Singapore, Singapore Imprint: Springer Verlag, Singapore ISBN-13: 9789811517389, 978-9811517389 Synopsis This book is a posthumous publication of a classic by Prof. Shoshichi Kobayashi, who taught at [url] 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 major topic of this book, is discussed at great length. The theorem is a most beautiful and deep result in differential geometry. It yields a relation between the integral of the Gaussian curvature over a given oriented closed surface S and the topology of S in terms of its Euler number (S). Here again, many illustrations are provided to facilitate the reader's understanding. Chapter 5, Minimal Surfaces, requires some elementary knowledge of complex analysis. However, the author retained the introductory nature of this book and focused on detailed explanations of the examples of minimal surfaces given in Chapter 2.
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End Time: 2024-12-23T15:35:07.000Z
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Book Title: Differential Geometry of Curves and Surfaces
Number of Pages: 192 Pages
Language: English
Publication Name: Differential Geometry of Curves and Surfaces
Publisher: Springer Verlag, Singapore
Publication Year: 2019
Subject: Mathematics
Item Height: 235 mm
Item Weight: 326 g
Type: Textbook
Author: Shoshichi Kobayashi
Series: Springer Undergraduate Mathematics Series
Item Width: 155 mm
Format: Paperback
