Lectures on classical differential geometry / by Dirk J. Struik.
Series Addison-Wesley mathematics seriesEditor: Cambridge, Mass. : Addison-Wesley, 1950Descripción: viii, 221 p. ; 24 cmOtro título: Differential geometryOtra clasificación: 53.0XPreface v Bibliography vii Chapter 1. Curves [1] 1-1 Analytic representation [1] 1-2 Arc length, tangent [5] 1-3 Osculating plane [10] 1-4 Curvature [13] 1-5 Torsion [15] 1-6 Formulas of Frenet [18] 1-7 Contact [23] 1-8 Natural equations [26] 1-9 Helices [33] 1-10 General solution of the natural equations [36] 1-11 Evolutes and involutes [39] 1-12 Imaginary curves [44] 1-13 Ovals [47] 1-14 Monge [53] Chapter 2. Elementary Theory of Surfaces [55] 2-1 Analytical representation [55] 2-2 First fundamental form [58] 2-3 Normal, tangent plane [62] 2-4 Developable surfaces [66] 2-5 Second fundamental form. Meusnier’s theorem [73] 2-6 Euler’s theorem [77] 2-7 Dupin’s indicatrix [83] 2-8 Some surfaces [86] 2-9 A geometrical interpretation of asymptotic and curvature lines [93] 2-10 Conjugate directions [96] 2- 11 Triply orthogonal systems of surfaces [99] Chapter 3. The Fundamental Equations [105] 3- 1 Gauss [105] 3-2 The equations of Gauss-Weingarten [106] 3-3 The theorem of Gauss and the equations of Codazzi [110] 3-4 Curvilinear coordinates in space [115] 3-5 Some applications of the Gauss and the Codazzi equations [120] 3-6 The fundamental theorem of surface theory [124] Chapter 4. Geometry on a Surface [127] 4-1 Geodesic (tangential) curvature [127] 4-2 Geodesics [131] 4-3 Geodesic coordinates [136] 4-4 Geodesics as extremals of a variational problem [140] 4-5 Surfaces of constant curvature [144] 4-6 Rotation surfaces of constant curvature [147] 4-7 Non-Euclidean geometry [150] 4- 8 The Gauss-Bonnet theorem [153] Chapter 5. Some Special Subjects [162] 5- 1 Envelopes [162] 5-2 Conformal mapping [168] 5-3 Isometric and geodesic mapping [175] 5-4 Minimal surfaces [182] 5-5 Ruled surfaces [189] 5-6 Imaginaries in surface theory [195] Some Problems and Propositions [201] Answers to Problems [205] Index [215]
| Item type | Home library | Shelving location | Call number | Materials specified | Status | Date due | Barcode | Course reserves |
|---|---|---|---|---|---|---|---|---|
Libros
|
Instituto de Matemática, CONICET-UNS | Libros ordenados por tema | 53 St927 (Browse shelf) | Available | A-2072 |
Hoja suelta: Errata.
Preface v --
Bibliography vii --
Chapter 1. Curves [1] --
1-1 Analytic representation [1] --
1-2 Arc length, tangent [5] --
1-3 Osculating plane [10] --
1-4 Curvature [13] --
1-5 Torsion [15] --
1-6 Formulas of Frenet [18] --
1-7 Contact [23] --
1-8 Natural equations [26] --
1-9 Helices [33] --
1-10 General solution of the natural equations [36] --
1-11 Evolutes and involutes [39] --
1-12 Imaginary curves [44] --
1-13 Ovals [47] --
1-14 Monge [53] --
Chapter 2. Elementary Theory of Surfaces [55] --
2-1 Analytical representation [55] --
2-2 First fundamental form [58] --
2-3 Normal, tangent plane [62] --
2-4 Developable surfaces [66] --
2-5 Second fundamental form. Meusnier’s theorem [73] --
2-6 Euler’s theorem [77] --
2-7 Dupin’s indicatrix [83] --
2-8 Some surfaces [86] --
2-9 A geometrical interpretation of asymptotic and curvature lines [93] --
2-10 Conjugate directions [96] --
2- 11 Triply orthogonal systems of surfaces [99] --
Chapter 3. The Fundamental Equations [105] --
3- 1 Gauss [105] --
3-2 The equations of Gauss-Weingarten [106] --
3-3 The theorem of Gauss and the equations of Codazzi [110] --
3-4 Curvilinear coordinates in space [115] --
3-5 Some applications of the Gauss and the Codazzi equations [120] --
3-6 The fundamental theorem of surface theory [124] --
Chapter 4. Geometry on a Surface [127] --
4-1 Geodesic (tangential) curvature [127] --
4-2 Geodesics [131] --
4-3 Geodesic coordinates [136] --
4-4 Geodesics as extremals of a variational problem [140] --
4-5 Surfaces of constant curvature [144] --
4-6 Rotation surfaces of constant curvature [147] --
4-7 Non-Euclidean geometry [150] --
4- 8 The Gauss-Bonnet theorem [153] --
Chapter 5. Some Special Subjects [162] --
5- 1 Envelopes [162] --
5-2 Conformal mapping [168] --
5-3 Isometric and geodesic mapping [175] --
5-4 Minimal surfaces [182] --
5-5 Ruled surfaces [189] --
5-6 Imaginaries in surface theory [195] --
Some Problems and Propositions [201] --
Answers to Problems [205] --
Index [215] --
MR, MR0036551
Click on an image to view it in the image viewer
There are no comments on this title.