The local theory of the second chapter curve of differential geometry

Chapter Two, the local theory of the curve

2.1 Concept of the curve

A discussion of non-regular curves:

, which is an irregular point (a sharp point), and it is an irregular curve.

Intuitively, discontinuities, outliers, nodes (intersections), cusp points are non-regular points.

It is recorded that when the same curve is represented by different parametric equations, the same curve may appear as a regular curve under one parameter representation and a non-regular curve under another parameter representation.

To give a simple example:

The parametric equation of a circle can be expressed as:

It can also be expressed as:

It can be seen that the curve represented by the first parametric equation is a regular curve, and the curve represented by the second parametric equation is a non-regular curve.

2.2 Planar curve

2.3 E3 curve

The basic theorem of 2.4 curve theory

The local theory of the second chapter curve of differential geometry