Cargando…
Elementary differential geometry /
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
New York :
Academic Press,
[1966]
|
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Front Cover; Elementary Differential Geometry; Copyright Page; Preface; Table of Contents; Introduction; Chapter I. Calculus on Euclidean Space; 1 Euclidean Space; 2 Tangent Vectors; 3 Directional Derivatives; 4 Curves in E; 5 1-Forms; 6 Differential Forms; 7 Mappings; 8 Summary; Chapter II. Frame Fields; 1 Dot Product; 2 Curves; 3 The Frenet Formulas; 4 Arbitrary-Speed Curves; 5 Covariant Derivatives; 6 Frame Fields; 7 Connection Forms; 8 The Structural Equations; 9 Summary; Chapter III. Euclidean Geometry; 1 Isometries of E; 2 The Derivative Map of an Isometry; 3 Orientation.
- 4 Euclidean Geometry5 Congruence of Curves; 6 Summary; Chapter IV. Calculus on a Surface; 1 Surfaces in E; 2 Patch Computations; 3 Differentiable Functions and Tangent Vectors; 4 Differential Forms on a Surface; 5 Mappings of Surfaces; 6 Integration of Forms; 7 Topological Properties of Surfaces; 8 Manifolds; 9 Summary; Chapter V. Shape Operators; 1 The Shape Operator of M c E; 2 Normal Curvature; 3 Gaussian Curvature; 4 Computational Techniques; 5 Special Curves in a Surface; 6 Surfaces of Revolution; 7 Summary; Chapter VI. Geometry of Surfaces in E; 1 The Fundamental Equations.
- 2 Form Computations3 Some Global Theorems; 4 Isometries and Local Isometries; 5 Intrinsic Geometry of Surfaces in E; 6 Orthogonal Coordinates; 7 Integration and Orientation; 8 Congruence of Surfaces; 9 Summary; Chapter VII. Riemannian Geometry; 1 Geometric Surfaces; 2 Gaussian Curvature; 3 Covariant Derivative; 4 Geodesies; 5 Length-Minimizing Properties of Geodesies; 6 Curvature and Conjugate Points; 7 Mappings that Preserve Inner Products; 8 The Gauss-Bonnet Theorem; 9 Summary; Bibliography; Answers to Odd-Numbered Exercises; INDEX.