《微分几何中的初等论题》由J.A.Thorpe（索普）著，主要内容：This book develops the geometry of n-dimensional surfaces in(n+1)． space．It iS designed for a l-semester difrorential geometry course at the junior-senior Ievel．It draws significantly on the contemporary student's knowledge oflinear algebra，multivariate calculus，and differential equations． thereby solidifying the student’S understanding of these SUbjects．Indeed． one of the reasons that a course in difierential geometry iS SO valuable at this level is that it does turn out students with a thorough understanding of several variable calcuills.

Chapter 1

Graphs and Level Sets

Chapter 2

Vector Fields

Chapter 3

The Tangent Space

Chapter 4

Surfaces

Chapter 5

Vector Fields on Surfaces; Orientation

Chapter 6

The Gauss Map

Chapter 7

Geodesics

Chapter 8

Parallel Transport

Chapter 9

The Weingarten Map

Chapter 10

Curvature of Plane Curves

Chapter l 1

Arc Length and Line Integrals

Chapter 12

Curvature of Surfaces

Chapter 13

Convex Surfaces

Chapter 14

Parametrized Surfaces

Chapter 15

Local Equivalence of Surfaces and Parametrized

Surfaces

Chapter 16

Focal Points

Chapter 17

Surface Area and Volume

Chapter 18

Minimal Surfaces

Chapter 19

The Exponential Map

Chapter 20

Surfaces with Boundary

Chapter 21

The Gauss-Bonnet Theorem

Chapter 22

Rigid Motions and Congruence

Chapter 23

Isometries

Chapter 24

Riemannian Metrics

Bibliography

Notational Index

Subject Index