Elementary differential geometry / Barrett O'Neill.
Editor: New York : Academic Press, c1966Descripción: viii, 411 p. : il. ; 24 cm. + 1 suplemento (9 p.)Tema(s): Geometry, DifferentialOtra clasificación: 53-01Contents Preface v Introduction [1] Chapter I. Calculus on Euclidean Space 1. Euclidean Space [3] 2. Tangent Vectors [6] 3. Directional Derivatives [11] 4. Curves in E8 [15] 5. 1-Forms [22] 6. Differential Forms [26] 7. Mappings [32] 8. Summary [41] Chapter II. Frame Fields 1. Dot Product [42] 2. Curves [51] 3. The Frenet Formulas [56] 4. Arbitrary-Speed Curves [66] 5. Covariant Derivatives [77] 6. Frame Fields [81] 7. Connection Forms [85] 8. The Structural Equations [91] 9. Summary [96] Chapter III. Euclidean Geometry 1. Isometries of E3 [98] 2. The Derivative Map of an Isometry [104] 3. Orientation [107] 4. Euclidean Geometry [112] 5. Congruence of Curves [116] 6. Summary [123] Chapter IV. Calculus on a Surface 1. Surfaces in E3 [124] 2. Patch Computations [133] 3. Differentiable Functions and Tangent Vectors [143] 4. Differential Forms on a Surface [152] 5. Mappings of Surfaces [158] 6. Integration of Forms [167] 7. Topological Properties of Surfaces [176] 8. Manifolds [182] 9. Summary [187] Chapter V. Shape Operators 1. The Shape Operator of M E3 [189] 2. Normal Curvature [195] 3. Gaussian Curvature [203] 4. Computational Techniques [210] 5. Special Curves in a Surface [223] 6. Surfaces of Revolution [234] 7. Summary [244] Chapter VI. Geometry of Surfaces in E3 1. The Fundamental Equations [245] 2. Form Computations [251] 3. Some Global Theorems [256] 4. Isometries and Local Isometries [263] 5. Intrinsic Geometry of Surfaces in E3 [271] 6. Orthogonal Coordinates [276] 7. Integration and Orientation [280] 8. Congruence of Surfaces [297] 9. Summary [303] Chapter VII. Riemannian Geometry 1. Geometric Surfaces [304] 2. Gaussian Curvature [310] 3. Covariant Derivative [318] 4. Geodesics [326] 5. Length-Minimizing Properties of Geodesics [339] 6. Curvature and Conjugate Points [352] 7. Mappings that Preserve Inner Products [362] 8. The Gauss-Bonnet Theorem [372] 9. Summary [389] Bibliography [391] Answers to Odd-Numbered Exercises [393] Index [405]
| Item type | Home library | Call number | Materials specified | Status | Date due | Barcode | Course reserves |
|---|---|---|---|---|---|---|---|
Libros
|
Instituto de Matemática, CONICET-UNS | 53 On58 (Browse shelf) | Available | A-2517 |
Suplemento: Answers to even-numbered problems.
Bibliografía: p. [391].
Contents --
Preface v --
Introduction [1] --
Chapter I. Calculus on Euclidean Space --
1. Euclidean Space [3] --
2. Tangent Vectors [6] --
3. Directional Derivatives [11] --
4. Curves in E8 [15] --
5. 1-Forms [22] --
6. Differential Forms [26] --
7. Mappings [32] --
8. Summary [41] --
Chapter II. Frame Fields --
1. Dot Product [42] --
2. Curves [51] --
3. The Frenet Formulas [56] --
4. Arbitrary-Speed Curves [66] --
5. Covariant Derivatives [77] --
6. Frame Fields [81] --
7. Connection Forms [85] --
8. The Structural Equations [91] --
9. Summary [96] --
Chapter III. Euclidean Geometry --
1. Isometries of E3 [98] --
2. The Derivative Map of an Isometry [104] --
3. Orientation [107] --
4. Euclidean Geometry [112] --
5. Congruence of Curves [116] --
6. Summary [123] --
Chapter IV. Calculus on a Surface --
1. Surfaces in E3 [124] --
2. Patch Computations [133] --
3. Differentiable Functions and Tangent Vectors [143] --
4. Differential Forms on a Surface [152] --
5. Mappings of Surfaces [158] --
6. Integration of Forms [167] --
7. Topological Properties of Surfaces [176] --
8. Manifolds [182] --
9. Summary [187] --
Chapter V. Shape Operators --
1. The Shape Operator of M E3 [189] --
2. Normal Curvature [195] --
3. Gaussian Curvature [203] --
4. Computational Techniques [210] --
5. Special Curves in a Surface [223] --
6. Surfaces of Revolution [234] --
7. Summary [244] --
Chapter VI. Geometry of Surfaces in E3 --
1. The Fundamental Equations [245] --
2. Form Computations [251] --
3. Some Global Theorems [256] --
4. Isometries and Local Isometries [263] --
5. Intrinsic Geometry of Surfaces in E3 [271] --
6. Orthogonal Coordinates [276] --
7. Integration and Orientation [280] --
8. Congruence of Surfaces [297] --
9. Summary [303] --
Chapter VII. Riemannian Geometry --
1. Geometric Surfaces [304] --
2. Gaussian Curvature [310] --
3. Covariant Derivative [318] --
4. Geodesics [326] --
5. Length-Minimizing Properties of Geodesics [339] --
6. Curvature and Conjugate Points [352] --
7. Mappings that Preserve Inner Products [362] --
8. The Gauss-Bonnet Theorem [372] --
9. Summary [389] --
Bibliography [391] --
Answers to Odd-Numbered Exercises [393] --
Index [405] --
MR, 34 #3444
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