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007			cr nn 008mamaa
008			230419s2013 sz | s |||| 0|eng d
020			_a9783031024054
024	7		_a10.1007/978-3-031-02405-4 _2doi
040			_aES-MaUEC _bspa _cES-MaUEC _dES-MaUEC
050		4	_aQA477 _b2013 EB
100	1		_aGarcía-Río, Eduardo _eautor _4aut _4http://id.loc.gov/vocabulary/relators/aut _9687522
245	1	0	_aApplications of Affine and Weyl Geometry _cby Eduardo García-Río, Peter Gilkey, Stana Nikčević, Ramón Vázquez-Lorenzo
250			_a1st edition 2013
264		1	_aCham _bSpringer International Publishing _c2013
300			_a1 recurso en línea (XV, 152 páginas)
336			_atexto _btxt _2rdacontent
337			_aelectrónico _bc _2rdamedia
338			_arecurso electrónico _bcr _2rdacarrier
347			_aarchivo de texto _bPDF
490	0		_aSynthesis Lectures on Mathematics & Statistics _x1938-1751
505	0		_aBasic Notions and Concepts -- The Geometry of Deformed Riemannian Extensions -- The Geometry of Modified Riemannian Extensions -- (para)-Kähler--Weyl Manifolds.
520			_aPseudo-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 possible to 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.
988			_aSynthesis Collection of Technology_2013
650		7	_2embne _9160059 _aGeometría afín
650		7	_2embne _9677848 _aVariedades riemannianas
700	1		_aGilkey, Peter B. _eautor _4aut _4http://id.loc.gov/vocabulary/relators/aut _9686447
700	1		_aNikčević, Stana _eautor _4aut _4http://id.loc.gov/vocabulary/relators/aut _9688138
700	1		_aVázquez-Lorenzo, Ramón _eautor _4aut _4http://id.loc.gov/vocabulary/relators/aut _9686449
776	0	8	_iPrinted edition: _z9783031012778
776	0	8	_iPrinted edition: _z9783031035333
856	4	0	_uhttps://go.openathens.net/redirector/universidadeuropea.es?url=https://doi.org/10.1007/978-3-031-02405-4 _zAcceso a este recurso digital (usuarios Universidad Europea de Madrid)
942			_2lcc _cLE
998			_b04/2023 _dz _eIG _zSI