國立虎尾科技大學 |

Differential Geometry of Curves and Surfaces

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Differential Geometry of Curves and Surfaces/ by Shoshichi Kobayashi.
作者:	Kobayashi, Shoshichi.
面頁冊數:	XII, 192 p. 1 illus.online resource. :
Contained By:	Springer Nature eBook
標題:	Differential geometry. -
電子資源:	https://doi.org/10.1007/978-981-15-1739-6
ISBN:	9789811517396

Differential Geometry of Curves and Surfaces
Kobayashi, Shoshichi.

Differential Geometry of Curves and Surfaces[electronic resource] /by Shoshichi Kobayashi. - 1st ed. 2019. - XII, 192 p. 1 illus.online resource. - Springer Undergraduate Mathematics Series,1615-2085. - Springer Undergraduate Mathematics Series,.

Plane Curves and Space Curves -- Local Theory of Surfaces in the Space -- Geometry of Surfaces -- The Gauss-Bonnet Theorem -- Minimal Surfaces. .

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 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 χ(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. .

ISBN: 9789811517396

Standard No.: 10.1007/978-981-15-1739-6doiSubjects--Topical Terms:

882213
Differential geometry.

LC Class. No.: QA641-670

Dewey Class. No.: 516.36

Differential Geometry of Curves and Surfaces
LDR:03317nam a22003975i 4500 001 1006285
003 DE-He213
005 20200705160427.0
007 cr nn 008mamaa
008 210106s2019 si | s |||| 0|eng d
020 $a 9789811517396 $9 978-981-15-1739-6
024 7 $a 10.1007/978-981-15-1739-6 $2 doi
035 $a 978-981-15-1739-6
050 4 $a QA641-670
072 7 $a PBMP $2 bicssc
072 7 $a MAT012030 $2 bisacsh
072 7 $a PBMP $2 thema
082 0 4 $a 516.36 $2 23
100 1 $a Kobayashi, Shoshichi. $e author. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1299807
245 1 0 $a Differential Geometry of Curves and Surfaces $h [electronic resource] / $c by Shoshichi Kobayashi.
250 $a 1st ed. 2019.
264 1 $a Singapore : $b Springer Singapore : $b Imprint: Springer, $c 2019.
300 $a XII, 192 p. 1 illus. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
490 1 $a Springer Undergraduate Mathematics Series, $x 1615-2085
505 0 $a Plane Curves and Space Curves -- Local Theory of Surfaces in the Space -- Geometry of Surfaces -- The Gauss-Bonnet Theorem -- Minimal Surfaces. .
520 $a 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 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 χ(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. .
650 0 $a Differential geometry. $3 882213
650 0 $a Mathematical analysis. $3 527926
650 0 $a Analysis (Mathematics). $3 1253570
650 0 $a Manifolds (Mathematics). $3 1051266
650 0 $a Complex manifolds. $3 676705
650 1 4 $a Differential Geometry. $3 671118
650 2 4 $a Analysis. $3 669490
650 2 4 $a Manifolds and Cell Complexes (incl. Diff.Topology). $3 668590
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9789811517389
776 0 8 $i Printed edition: $z 9789811517402
830 0 $a Springer Undergraduate Mathematics Series, $x 1615-2085 $3 1255356
856 4 0 $u https://doi.org/10.1007/978-981-15-1739-6
912 $a ZDB-2-SMA
912 $a ZDB-2-SXMS
950 $a Mathematics and Statistics (SpringerNature-11649)
950 $a Mathematics and Statistics (R0) (SpringerNature-43713)