| 期刊全称 | Applications of Affine and Weyl Geometry | | 影响因子2023 | Eduardo García-Río,Peter Gilkey,Ramón Vázquez-Lore | | 视频video | | | 学科分类 | Synthesis Lectures on Mathematics & Statistics | | 图书封面 |  | | 影响因子 | Pseudo-Riemannian geometry is, to a large extent, the study of the Levi-Civita connection, which is the unique torsion-free connection compatible with the metric structure. There are, however, other affine connections which arise in different contexts, such as conformal geometry, contact structures, Weyl structures, and almost Hermitian geometry. In this book, we reverse this point of view and instead associate an auxiliary pseudo-Riemannian structure of neutral signature to certain affine connections and use this correspondence to study both geometries. We examine Walker structures, Riemannian extensions, and Kähler--Weyl geometry from this viewpoint. This book is intended to be accessible to mathematicians who are not expert in the subject and to students with a basic grounding in differential geometry. Consequently, the first chapter contains a comprehensive introduction to the basic results and definitions we shall need---proofs are included of many of these results to make it as self-contained as possible. Para-complex geometry plays an important role throughout the book and consequently is treated carefully in various chapters, as is the representation theory underlying vario | | Pindex | Book 2013 |
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发表于 2025-3-21 19:07:56
