Differential Geometry Exercise Book

Author: Yang Wenmao / Fu Chaojin / Cheng Xinyue (editors)
Publisher:
Publish Date: 2005-01-01
Features: Differential geometry is an important branch of mathematics, a discipline that studies the geometry of spatial forms using calculus as a tool. Classical differential geometry mainly includes the theory of curves and surfaces. This book serves as a teaching reference for differential geometry courses in higher education institutions. It systematically introduces the fundamental theories and exercises of curves and surfaces in three-dimensional Euclidean space, with a focus on local geometric properties, but also touches upon some global geometric properties. The book is divided into four chapters. Chapter 1 serves as prerequisite knowledge, introducing algebraic operations on vectors and the differential and integral calculus of vector functions. Chapter 2 presents the basic theory of curves, including fundamental formulas for curves, the existence and uniqueness theorem for curves, and various special curves. Chapter 3 discusses the basic theory of surfaces, including the first, second, and third fundamental forms of surfaces, as well as various curvatures related to surfaces and special types of surfaces on them. Chapter 4 briefly introduces some global theories and exercises related to curves and surfaces. When presenting the content of geometric theories, this book strives to be comprehensive, systematic, and highly concise, often using tables to illustrate the intrinsic connections between related concepts.