Includes bibliographical references (p. -410) and indexes.
Preface.- I. Manifolds, Normal Frames and Riemannian Coordinates.- II. Existence, Uniqueness and Construction of Normal Frames and Coordinates for Linear Connections.- III. Normal Frames and Coordinates for Derivations on Differentiable Manifolds.- IV. Normal Frames in Vector Bundles.- V. Normal Frames for Connections on Differentiable Fibre Bundles.- Bibliography.- Index.
(source: Nielsen Book Data)
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, a review of the existing results and an introduction to some new ideas and developments. Practically all existing essential results and methods concerning normal frames and coordinates can be found in the book. Most of the results are presented in 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 of their parts can be used independently for other tasks. (source: Nielsen Book Data)