Handbook of Normal Frames and Coordinates

1. Front Matter

   Pages i-xvi

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2. Manifolds, Normal Frames and Riemannian Coordinates

   Pages 1-71

3. Existence, Uniqueness and Construction of Normal Frames and Coordinates for Linear Connections

   Pages 73-139

4. Normal Frames and Coordinates for Derivations on Differentiable Manifolds

   Pages 141-211

5. Normal Frames in Vector Bundles

   Pages 213-331

6. Normal Frames for Connections on Differentiable Fibre Bundles

   Pages 333-400

7. Back Matter

   Pages 401-441

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The main subject of this book is an up-to-date and in-depth survey of the theory of normal frames and coordinates in di?erential geometry. The existing results, as well as new ones obtained lately by the author, on the theme are presented. The text is so organized that it can serve equally well as a reference manual, introduction to and review of the current research on the topic. Correspondingly, the possible audience ranges from graduate and post-graduate students to sci- tists working in di?erential geometry and theoretical/mathematical physics. This is re?ected in the bibliography which consists mainly of standard (text)books and journal articles. The present monograph is the ?rst attempt for collecting the known facts concerting normal frames and coordinates into a single publication. For that r- son, the considerations and most of the proofs are given in details. Conventionally local coordinates or frames, which can be holonomic or not, are called normal if in them the coe?cients of a linear connection vanish on some subset, usually a submanifold, of a di?erentiable manifold. Until recently the ex- tence of normal frames was known (proved) only for symmetric linear connections on submanifolds of a manifold. Now the problems concerning normal frames for derivationsof thetensor algebraovera di?erentiablemanifoldarewellinvestigate; in particular they completely cover the exploration of normal frames for arbitrary linear connections on a manifold. These rigorous results are important in conn- tion with some physical applications.

• curvature
• differential geometry
• fibre bundle
• manifold
• normal frame
• vector bundle

From the reviews:

“This is a careful and rather comprehensive presentation of theory and methods related to normal frames in differential geometry. … The book is carefully written, provides a good overview, and contains many interesting aspects not available otherwise. It is a valuable addition to the literature on connections in differential geometry.” (M. Kunzinger, Monatshefte für Mathematik, Vol. 154 (1), May, 2008)

• Institute for Nuclear Research and Nuclear Energy, Sofia, Bulgaria

  Bozhidar Z. Iliev

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