Handbook of normal frames and coordinates

Abstract

The main subject of the book is an up-to-date and in-depth survey of the theory of normal frames and coordinates in differential geometry. The book can be used as a reference manual, review of the existing results and introduction to some new ideas and developments. In the book can be found practically all existing essential results and methods concerning normal frames and coordinates. Most of the results are represented in full detail with full, in some cases new, proofs. All classical results are expanded and generalized in various directions. Theorems of existence, uniqueness and, possibly, holonomicity of the normal frames and coordinates are proved; mostly, the proofs are constructive and some their parts can be used independently for other tasks. Besides published results, their extensions and generalizations, the book contains completely new results which appear for the first time.