Differential Geometry of Curves and Surfaces: First Edition

Main subject categories: • Differential geometry • Analysis on manifolds • Fundamental equations of surfaces • Curves in n-dimensional space • Surfaces in n-dimensional space

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 Re.
Abstract: 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 Re