Aspects of Differential Geometry IV (Record no. 85137)
[ view plain ]
| 000 -LEADER | |
|---|---|
| fixed length control field | 04347nam a22005655i 4500 |
| 001 - CONTROL NUMBER | |
| control field | 978-3-031-02416-0 |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20240730163926.0 |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 220601s2019 sz | s |||| 0|eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| ISBN | 9783031024160 |
| -- | 978-3-031-02416-0 |
| 082 04 - CLASSIFICATION NUMBER | |
| Call Number | 510 |
| 100 1# - AUTHOR NAME | |
| Author | Calviño-Louzao, Esteban. |
| 245 10 - TITLE STATEMENT | |
| Title | Aspects of Differential Geometry IV |
| 250 ## - EDITION STATEMENT | |
| Edition statement | 1st ed. 2019. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Number of Pages | XVII, 149 p. |
| 490 1# - SERIES STATEMENT | |
| Series statement | Synthesis Lectures on Mathematics & Statistics, |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Remark 2 | Preface -- Acknowledgments -- An Introduction to Affine Geometry -- The Geometry of Type A Models -- The Geometry of Type B Models -- Applications of Affine Surface Theory -- Bibliography -- Authors' Biographies -- Index . |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc | Book IV continues the discussion begun in the first three volumes. Although it is aimed at first-year graduate students, it is also intended to serve as a basic reference for people working in affine differential geometry. It also should be accessible to undergraduates interested in affine differential geometry. We are primarily concerned with the study of affine surfaces {which} are locally homogeneous. We discuss affine gradient Ricci solitons, affine Killing vector fields, and geodesic completeness. Opozda has classified the affine surface geometries which are locally homogeneous; we follow her classification. Up to isomorphism, there are two simply connected Lie groups of dimension 2. The translation group ℝ² is Abelian and the �������� + ���� group\index{ax+b group} is non-Abelian. The first chapter presents foundational material. The second chapter deals with Type ���� surfaces. These are the left-invariant affine geometries on ℝ². Associating to each Type ���� surface the space of solutions to the quasi-Einstein equation corresponding to the eigenvalue ����=-1$ turns out to be a very powerful technique and plays a central role in our study as it links an analytic invariant with the underlying geometry of the surface. The third chapter deals with Type ���� surfaces; these are the left-invariant affine geometries on the �������� + ���� group. These geometries form a very rich family which is only partially understood. The only remaining homogeneous geometry is that of the sphere ����². The fourth chapter presents relations between the geometry of an affine surface and the geometry of the cotangent bundle equipped with the neutral signature metric of the modified Riemannian extension. |
| 700 1# - AUTHOR 2 | |
| Author 2 | García-Río, Eduardo. |
| 700 1# - AUTHOR 2 | |
| Author 2 | Gilkey, Peter. |
| 700 1# - AUTHOR 2 | |
| Author 2 | Park, JeongHyeong. |
| 700 1# - AUTHOR 2 | |
| Author 2 | Vázquez-Lorenzo, Ramón. |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | https://doi.org/10.1007/978-3-031-02416-0 |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) | |
| Koha item type | eBooks |
| 264 #1 - | |
| -- | Cham : |
| -- | Springer International Publishing : |
| -- | Imprint: Springer, |
| -- | 2019. |
| 336 ## - | |
| -- | text |
| -- | txt |
| -- | rdacontent |
| 337 ## - | |
| -- | computer |
| -- | c |
| -- | rdamedia |
| 338 ## - | |
| -- | online resource |
| -- | cr |
| -- | rdacarrier |
| 347 ## - | |
| -- | text file |
| -- | |
| -- | 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 |
No items available.