{"product_id":"differential-geometry-of-curves-and-surfaces-paperback","title":"Differential Geometry of Curves and Surfaces - Paperback","description":"\u003cp\u003eby \u003cb\u003eShoshichi Kobayashi\u003c\/b\u003e (Author), \u003cb\u003eEriko Shinozaki Nagumo\u003c\/b\u003e (Translator), \u003cb\u003eMakiko Sumi Tanaka\u003c\/b\u003e (Translator)\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eThis 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. \u003c\/p\u003e \u003cp\u003eThere 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. \u003c\/p\u003e \u003cp\u003eChapter 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 \u003ci\u003eK\u003c\/i\u003e and the mean curvature \u003ci\u003eH\u003c\/i\u003e --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\u003cb\u003e \u003c\/b\u003etheorem, 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 \u003ci\u003eS\u003c\/i\u003e and the topology of \u003ci\u003eS\u003c\/i\u003e in terms of its Euler number\u003cb\u003e \u003c\/b\u003eχ(\u003ci\u003eS\u003c\/i\u003e). 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. \u003c\/p\u003e\u003ch3\u003eAuthor Biography\u003c\/h3\u003e\u003cp\u003eProfessor Shoshichi Kobayashi was a Professor Emeritus at University of California, Berkeley. He passed away on August 29 in 2012. He was a student of Professor Kentaro Yano at the University of Tokyo. He was one of famous differential geometers not only in Japan but also in the world. He wrote 15 books both in Japanese and in English.\u003c\/p\u003e\u003cdiv\u003e\n\u003cstrong\u003eNumber of Pages:\u003c\/strong\u003e 192\u003c\/div\u003e\u003cdiv\u003e\n\u003cstrong\u003eDimensions:\u003c\/strong\u003e 0.44 x 9.21 x 6.14 IN\u003c\/div\u003e\u003cdiv\u003e\n\u003cstrong\u003eIllustrated:\u003c\/strong\u003e Yes\u003c\/div\u003e\u003cdiv\u003e\n\u003cstrong\u003ePublication Date:\u003c\/strong\u003e November 25, 2019\u003c\/div\u003e","brand":"Books by splitShops","offers":[{"title":"Default Title","offer_id":51792520085792,"sku":"9789811517389","price":72.88,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0974\/9764\/5344\/files\/ba0a95bbd1de90709445d5e042d0b49d.webp?v=1780703069","url":"https:\/\/ebocreations.com\/products\/differential-geometry-of-curves-and-surfaces-paperback","provider":"The E-Book Oasis LLC","version":"1.0","type":"link"}