Differential geometry of curves and surfaces
著者
書誌事項
Differential geometry of curves and surfaces
A.K. Peters, c2010
大学図書館所蔵 件 / 全12件
-
該当する所蔵館はありません
- すべての絞り込み条件を解除する
注記
Includes bibliographical references (p. 325-326) and index
内容説明・目次
内容説明
Students and professors of an undergraduate course in differential geometry will appreciate the clear exposition and comprehensive exercises in this book that focuses on the geometric properties of curves and surfaces, one- and two-dimensional objects in Euclidean space. The problems generally relate to questions of local properties (the properties observed at a point on the curve or surface) or global properties (the properties of the object as a whole). Some of the more interesting theorems explore relationships between local and global properties.
A special feature is the availability of accompanying online interactive java applets coordinated with each section. The applets allow students to investigate and manipulate curves and surfaces to develop intuition and to help analyze geometric phenomena.
目次
Preface
Acknowledgements
Plane Curves: Local Properties
Parameterizations
Position, Velocity, and Acceleration
Curvature
Osculating Circles, Evolutes, and Involutes
Natural Equations
Plane Curves: Global Properties
Basic Properties
Rotation Index
Isoperimetric Inequality
Curvature, Convexity, and the Four-Vertex Theorem
Curves in Space: Local Properties
Definitions, Examples, and Differentiation
Curvature, Torsion, and the Frenet Frame
Osculating Plane and Osculating Sphere
Natural Equations
Curves in Space: Global Properties
Basic Properties
Indicatrices and Total Curvature
Knots and Links
Regular Surfaces
Parametrized Surfaces
Tangent Planes and Regular Surfaces
Change of Coordinates
The Tangent Space and the Normal Vector
Orientable Surfaces
The First and Second Fundamental Forms
The First Fundamental Form
The Gauss Map
The Second Fundamental Form
Normal and Principal Curvatures
Gaussian and Mean Curvature
Ruled Surfaces and Minimal Surfaces
The Fundamental Equations of Surfaces
Tensor Notation
Gauss's Equations and the Christoffel Symbols
Codazzi Equations and the Theorema Egregium
The Fundamental Theorem of Surface Theory
Curves on Surfaces
Curvatures and Torsion
Geodesics
Geodesic Coordinates
Gauss-Bonnet Theorem and Applications
Intrinsic Geometry
Bibliography
「Nielsen BookData」 より