Applications of Affine and Weyl Geometry (Record no. 85130)
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| 000 -LEADER | |
|---|---|
| fixed length control field | 04660nam a22005415i 4500 |
| 001 - CONTROL NUMBER | |
| control field | 978-3-031-02405-4 |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20240730163922.0 |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 220601s2013 sz | s |||| 0|eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| ISBN | 9783031024054 |
| -- | 978-3-031-02405-4 |
| 082 04 - CLASSIFICATION NUMBER | |
| Call Number | 510 |
| 100 1# - AUTHOR NAME | |
| Author | García-Río, Eduardo. |
| 245 10 - TITLE STATEMENT | |
| Title | Applications of Affine and Weyl Geometry |
| 250 ## - EDITION STATEMENT | |
| Edition statement | 1st ed. 2013. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Number of Pages | XV, 152 p. |
| 490 1# - SERIES STATEMENT | |
| Series statement | Synthesis Lectures on Mathematics & Statistics, |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Remark 2 | Basic Notions and Concepts -- The Geometry of Deformed Riemannian Extensions -- The Geometry of Modified Riemannian Extensions -- (para)-Kähler--Weyl Manifolds. |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc | 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 various results. It is a feature of this book that, rather than as regarding para-complex geometry as an adjunct to complex geometry, instead, we shall often introduce the para-complex concepts first and only later pass to the complex setting. The second and third chapters are devoted to the study of various kinds of Riemannian extensions that associate to an affine structure on a manifold a corresponding metric of neutral signature on its cotangent bundle. These play a role in various questions involving the spectral geometry of the curvature operator and homogeneous connections on surfaces. The fourth chapter deals with Kähler--Weyl geometry, which lies, in a certain sense, midway between affine geometry and Kähler geometry. Another feature of the book is that we have tried wherever possibleto find the original references in the subject for possible historical interest. Thus, we have cited the seminal papers of Levi-Civita, Ricci, Schouten, and Weyl, to name but a few exemplars. We have also given different proofs of various results than those that are given in the literature, to take advantage of the unified treatment of the area given herein. |
| 700 1# - AUTHOR 2 | |
| Author 2 | Gilkey, Peter. |
| 700 1# - AUTHOR 2 | |
| Author 2 | Nikčević, Stana. |
| 700 1# - AUTHOR 2 | |
| Author 2 | Vázquez-Lorenzo, Ramón. |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | https://doi.org/10.1007/978-3-031-02405-4 |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) | |
| Koha item type | eBooks |
| 264 #1 - | |
| -- | Cham : |
| -- | Springer International Publishing : |
| -- | Imprint: Springer, |
| -- | 2013. |
| 336 ## - | |
| -- | text |
| -- | txt |
| -- | rdacontent |
| 337 ## - | |
| -- | computer |
| -- | c |
| -- | rdamedia |
| 338 ## - | |
| -- | online resource |
| -- | cr |
| -- | rdacarrier |
| 347 ## - | |
| -- | text file |
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| -- | rda |
| 650 #0 - SUBJECT ADDED ENTRY--SUBJECT 1 | |
| -- | Mathematics. |
| 650 #0 - SUBJECT ADDED ENTRY--SUBJECT 1 | |
| -- | Statistics . |
| 650 #0 - SUBJECT ADDED ENTRY--SUBJECT 1 | |
| -- | Engineering mathematics. |
| 650 14 - SUBJECT ADDED ENTRY--SUBJECT 1 | |
| -- | Mathematics. |
| 650 24 - SUBJECT ADDED ENTRY--SUBJECT 1 | |
| -- | Statistics. |
| 650 24 - SUBJECT ADDED ENTRY--SUBJECT 1 | |
| -- | Engineering Mathematics. |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE | |
| -- | 1938-1751 |
| 912 ## - | |
| -- | ZDB-2-SXSC |
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