Book Titles A First Course in Differential Geometry

Hardcover		A First Course in Differential Geometry
		ISBN: 1-57146-046-2 Year Published: 1997 Pages: 357 pages Binding: Hardcover Price: $45.00

Description: This book is designed to introduce differential geometry to beginning graduate students as well as advanced undergraduate students In the last couple of decades, differential geometry, along with other branches of mathematics, has been highly developed. In this book we will study only the traditional topics, namely, curves and surfaces in a three-dimensional Euclidean space E3. Unlike most classical books on the subject, however, more attention is paid here to the relationships between local and global properties, as opposed to local properties only. Although we restrict our attention to curves and surfaces in E3, most global theorems for curves and surfaces in this book can be extended to either higher dimensional spaces or more general curves and surfaces or both. Moreover, geometric interpretations are given along with analytic expressions. This will enable students to make use of geometric intuition, which is a precious tool for studying geometry and related problems. Contents: Chapter 1, Euclidean Spaces 1. PointSets 2. Differentiation and Integration 3. Vectors 4. Mappings 5. Linear Groups 6. Differential Forms 7. The Calculusof Variations Chapter 2, Curves 1. General Local Theory 2. Plane Curves 3. Global Theorems for Space Curves Chapter 3, Local Theory of Surfaces 1. Parametrizations 2. Functions and Fundamental Forms 3. Form of a Surface in a Neigborhood of a Point 4. Principal Curvatures, Asymptotic Curves, and Conjugate Directions 5. Mapping of Surfaces 6. Triply Orthogonal Systems, and the Theorems of Dupin and Liouville 7. Fundamental Equations 8. Ruled Surfaces and Minimal Surfaces 9. Levi-Civita Parallelism 10. Geodesics Chapter 4, Global Theory of Surfaces 1. Orientation of Surfaces 2. Surfaces of Constant Gaussian Curvature 3. The Gauss-Bonnet Formula 4. Exterior Differential Forms and a Uniqueness Theorem for Surfaces 5. Rigidity of Convex Surfaces and Minkowski’s Formulas 6. Some Translation and Symmetry Theorems 7. Uniqueness Theorems for Minkowski's and Christoffel’s Problems 8. Complete Surfaces Author: Chuan-Chih Hsiung To Order: Book Orders Book Sales - Great discounts on other popular titles!