Introduction to Differential Geometry of Space Curves and Surfaces: Differential Geometry of Curves and Surfaces

This book is about differential geometry of space curves and surfaces. The formulation and presentation are largely based on a tensor calculus approach. It can be used as part of a course on tensor calculus as well as a textbook or a reference for an intermediate-level course on differential geometry of curves and surfaces. The book is furnished with an index, extensive sets of exercises and many cross references, which are hyperlinked for the ebook users, to facilitate linking related concepts and sections. The book also contains a considerable number of 2D and 3D graphic illustrations to help the readers and users to visualize the ideas and understand the abstract concepts. We also provided an introductory chapter where the main concepts and techniques needed to understand the offered materials of differential geometry are outlined to make the book fairly self-contained and reduce the need for external references.

Table of Contents

1: Preliminaries
2: Curves in Space
3: Surfaces in Space
4: Curvature
5: Special Curves
6: Special Surfaces
7: Tensor Differentiation over Surfaces
8: Footnotes