LEADER 04292nam 22006615 450 001 9910360852603321 005 20200705160427.0 010 $a9789811517396 010 $a9811517398 024 7 $a10.1007/978-981-15-1739-6 035 $a(CKB)4100000009844812 035 $a(DE-He213)978-981-15-1739-6 035 $a(MiAaPQ)EBC5978848 035 $a(PPN)269145281 035 $a(MiAaPQ)EBC31872513 035 $a(Au-PeEL)EBL31872513 035 $a(EXLCZ)994100000009844812 100 $a20191113d2019 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aDifferential Geometry of Curves and Surfaces /$fby Shoshichi Kobayashi 205 $a1st ed. 2019. 210 1$aSingapore :$cSpringer Singapore :$cImprint: Springer,$d2019. 215 $a1 online resource (XII, 192 p. 1 illus.) 225 1 $aSpringer Undergraduate Mathematics Series,$x1615-2085 311 08$a9789811517389 311 08$a981151738X 327 $aPlane Curves and Space Curves -- Local Theory of Surfaces in the Space -- Geometry of Surfaces -- The Gauss-Bonnet Theorem -- Minimal Surfaces. . 330 $aThis book is a posthumous publication of a classic by Prof. Shoshichi Kobayashi, who taught at U.C. Berkeley for 50 years, recently translated by Eriko Shinozaki Nagumo and Makiko Sumi Tanaka. There are five chapters: 1. Plane Curves and Space Curves; 2. Local Theory of Surfaces in Space; 3. Geometry of Surfaces; 4. Gauss?Bonnet Theorem; and 5. Minimal Surfaces. Chapter 1 discusses local and global properties of planar curves and curves in space. Chapter 2 deals with local properties of surfaces in 3-dimensional Euclidean space. Two types of curvatures ? the Gaussian curvature K and the mean curvature H ?are introduced. The method of the moving frames, a standard technique in differential geometry, is introduced in the context of a surface in 3-dimensional Euclidean space. In Chapter 3, the Riemannian metric on a surface is introduced and properties determined only by the first fundamental form are discussed. The concept of a geodesic introduced in Chapter 2 is extensively discussed, and several examples of geodesics are presented with illustrations. Chapter 4 starts with a simple and elegant proof of Stokes? theorem for a domain. Then the Gauss?Bonnet theorem, the major topic of this book, is discussed at great length. The theorem is a most beautiful and deep result in differential geometry. It yields a relation between the integral of the Gaussian curvature over a given oriented closed surface S and the topology of S in terms of its Euler number ?(S). Here again, many illustrations are provided to facilitate the reader?s understanding. Chapter 5, Minimal Surfaces, requires some elementary knowledge of complex analysis. However, the author retained the introductory nature of this book and focused on detailed explanations of the examples of minimal surfaces given in Chapter 2. . 410 0$aSpringer Undergraduate Mathematics Series,$x1615-2085 606 $aGeometry, Differential 606 $aMathematical analysis 606 $aAnalysis (Mathematics) 606 $aManifolds (Mathematics) 606 $aComplex manifolds 606 $aDifferential Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M21022 606 $aAnalysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12007 606 $aManifolds and Cell Complexes (incl. Diff.Topology)$3https://scigraph.springernature.com/ontologies/product-market-codes/M28027 615 0$aGeometry, Differential. 615 0$aMathematical analysis. 615 0$aAnalysis (Mathematics). 615 0$aManifolds (Mathematics) 615 0$aComplex manifolds. 615 14$aDifferential Geometry. 615 24$aAnalysis. 615 24$aManifolds and Cell Complexes (incl. Diff.Topology). 676 $a516.36 700 $aKobayashi$b Shoshichi$4aut$4http://id.loc.gov/vocabulary/relators/aut$042069 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910360852603321 996 $aDifferential Geometry of Curves and Surfaces$91733854 997 $aUNINA