Content Introduction
"Avoid Differential Geometry": Chinese Science and Technology Classic Library (Mathematical Volume).
Book catalog
preamble
first chapter insteph
1.1 transformation group and subordinate geometric
1.2 Avoid transformation group and shooting group
1.3 affine flat curve Basic Theorem
1.4 Avine Space Curve Basic Theorem
1.5 Scruit Space Surface Discussion on the Currection
The Issue of the Problem
Chapter 2 Square Issues in the Symbient Plane Curve Theory
2.1 Blaschke inequality
2.2 MINKOWSKI-B? HMER Theorem
2.3 Six Key Point Theorem
2.2 Elliptic Curved Oval Line Related Theorem
2.5 Elliptical One isometric Properties
2.7 Sylvester's three-point problem
2.7 triangle maximum nature
exercises and theorem
Chapter 3, an affine band Geometric Structure
3.1 Transcon plane and affine surface normal relationship
3.2 moutard weaving surface
3.3 Main cutting woven donor
< P> 3.4? ech transformation 捌 捌 τ?exercises and theorem
Chapter 4, affine cast surface and imitation spinning direction
4.1 imitation The injection surface and its transformation
4.2 imitation rotating surface
4.3 generalized affine cast surface and imitation rotating surface
4.4 imitation rotary surface Some features
4.5 Imitation of the rotating surface
4.6 Imitation Rotating surface expansion
exercises and theorem
Chapter 5 Some relationships between the eminential surface theory and the surface of the project, the study of curved surfaces of the protrusion of the protrusions of the protracted lines
5.2 First type surface ( K)
5.3 Class Second Class Class (K)
5.4 Main Switch Something Face (-3)
5.5 Surface (1)
5.6 Surface (-1)
5.7 Surface (-1) Discussion
Exercise and Theorem
Appendix 1 Sound of Surface BONNET problem
1.6 About BONNET minimal surfaces
1.2 About a surface application of two plane friolation curve lines
1.3 Avinex minimal surface
1.4 under condition 1O, surface-friable curved curved surface
1.5 in case 2O of surface
Appendix 2 Division of aerial emulation of super cast surface and affine Super-rotation surface
2. Exquisite ultra-casting surface
2.2 affine super-rotation face
2.3 has different vertex curves imitation Transformation
Reference Bibliography
Preface
This classical differential geometry has been built early in the 1920s, published W, 1923 W, Blaschke's second volume of the "Differential Geometry" book, its content is an affine differential, soon, G, Fubini and E, CEECH, "shooting differential geometry" two rolls, these two differentiates The geometric formation is clearly based on Klein's geometric classification, and the method discussed is based on the basic form of gallss's surface, because of this, the geometric structure of the affine differential geometry is not like ordinary differential geometry. Obviously, intuitive, especially the relationship with the shooting differential geometry is not so clear, these two legacy issues have become the work goal of many mathematicians in the late 1920s, and their research results are rich in affine. The details of the differential geometry can be found in the detailed literature on the father and son, and the reference book is referred to in the book. For example, the expansion of the rotating surface in the three-dimensional antibody space is initially emerged in 1928, at the time The German geometry W, Siiss and books are independently and almost simultaneously solve this problem,
Noth of development, this development is not more than the monograph, and the author has, in view of this, Subjective film is the main foundation, with the main foundation of the research results in the two or three years of the past, written in cost book, public, in particular, first chapter and second chapter In addition to a few segments, it is taken from the original of Blaschke. The purpose is to introduce the reader to introduce the profile of the curve and surface theory of the faded differential geometry. It is also the foundation for the following three chapters, from the second The content of the chapter can also see the expansion of modern overall differential geometry, and the third chapter is written around a four-order conical surface around the surface, and it also clarifies the geometric structure of the emojun, especially Moutard. The main role in the fourth chapter, in the fourth chapter, the author introduces the imitation rotation of the imitation rotation according to its own way, it is seen in Appendix 2 according to its own way, and it is seen in Appendix 2, which must be pointed out: this theory involves the surface The Darboux curve and provide research foundations for the next chapter.