Many math books suffer from schizophrenia, this is another. On the one hand, it attempts to be a reference to the basic results on the flat rumanian manifolds. On the other hand, he tries to be a textbook that can be used for a second year graduation course.

My goal was to preserve the dominant second personality, but the reference character continued to emerge, especially at the end of the sections in the form of notes containing more advanced materials. To please this reference character, I will start by telling you a bit about the subject of the book, and then I will talk about the side of the textbook.

Flat raemannian manifold is a space that you can talk about geometry (such as distance, angle, curvature, "straight lines", etc.), and in addition, geometry is locally all one we all know and love, Euclidean geometry. This means that anyone anywhere in this space can provide coordinates so that Euclidean geometry rules are maintained with respect to these coordinates.

These coordinates are not valid in the entire area, so you can not conclude that the area is an euclidean space in itself. In this book, we are mainly concerned with the small flat riman complications, and unless we say otherwise, we use the term flat flat to mean a small flat rimmani complex.

It turns out that the most important fixed elements of flat openings are the core elements of a set.