000			04524nam a22004575i 4500
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007			cr nn 008mamaa
008			230419s2009 sz | s |||| 0|eng d
020			_a9783031023972
024	7		_a10.1007/978-3-031-02397-2 _2doi
040			_aES-MaUEC _bspa _cES-MaUEC _dES-MaUEC
050		4	_aQA613 _b2009 EB
100	1		_aGilkey, Peter B. _eautor _4aut _4http://id.loc.gov/vocabulary/relators/aut _9686447
245	1	4	_aThe Geometry of Walker Manifolds _cby Peter Gilkey, Miguel Brozos-Vázquez, Eduardo Garcia-Rio, Stana Nikčević, Ramón Vásquez-Lorenzo
250			_a1st edition 2009
264		1	_aCham _bSpringer International Publishing _c2009
300			_a1 recurso en línea (XVII, 159 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 Algebraic Notions -- Basic Geometrical Notions -- Walker Structures -- Three-Dimensional Lorentzian Walker Manifolds -- Four-Dimensional Walker Manifolds -- The Spectral Geometry of the Curvature Tensor -- Hermitian Geometry -- Special Walker Manifolds.
520			_aThis book, which focuses on the study of curvature, is an introduction to various aspects of pseudo-Riemannian geometry. We shall use Walker manifolds (pseudo-Riemannian manifolds which admit a non-trivial parallel null plane field) to exemplify some of the main differences between the geometry of Riemannian manifolds and the geometry of pseudo-Riemannian manifolds and thereby illustrate phenomena in pseudo-Riemannian geometry that are quite different from those which occur in Riemannian geometry, i.e. for indefinite as opposed to positive definite metrics. Indefinite metrics are important in many diverse physical contexts: classical cosmological models (general relativity) and string theory to name but two. Walker manifolds appear naturally in numerous physical settings and provide examples of extremal mathematical situations as will be discussed presently. To describe the geometry of a pseudo-Riemannian manifold, one must first understand the curvature of the manifold. We shall analyze a wide variety of curvature properties and we shall derive both geometrical and topological results. Special attention will be paid to manifolds of dimension 3 as these are quite tractable. We then pass to the 4 dimensional setting as a gateway to higher dimensions. Since the book is aimed at a very general audience (and in particular to an advanced undergraduate or to a beginning graduate student), no more than a basic course in differential geometry is required in the way of background. To keep our treatment as self-contained as possible, we shall begin with two elementary chapters that provide an introduction to basic aspects of pseudo-Riemannian geometry before beginning on our study of Walker geometry. An extensive bibliography is provided for further reading. Math subject classifications : Primary: 53B20 -- (PACS: 02.40.Hw) Secondary: 32Q15, 51F25, 51P05, 53B30, 53C50, 53C80, 58A30, 83F05, 85A04 Table of Contents: Basic Algebraic Notions / Basic Geometrical Notions / Walker Structures / Three-Dimensional Lorentzian Walker Manifolds / Four-Dimensional Walker Manifolds / The Spectral Geometry of the Curvature Tensor / Hermitian Geometry / Special Walker Manifolds.
988			_aSynthesis Collection of Technology_2009
650		7	_2embne-DP _9688136 _aVariedades algebraicas
650		7	_2embne _9677848 _aVariedades riemannianas
700	1		_aBrozos Vázquez, Miguel _eautor _4aut _4http://id.loc.gov/vocabulary/relators/aut _9688137
700	1		_aGarcía-Río, Eduardo _eautor _4aut _4http://id.loc.gov/vocabulary/relators/aut _9687522
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: _z9783031012693
776	0	8	_iPrinted edition: _z9783031035258
856	4	0	_uhttps://go.openathens.net/redirector/universidadeuropea.es?url=https://doi.org/10.1007/978-3-031-02397-2 _zAcceso a este recurso digital (usuarios Universidad Europea de Madrid)
942			_2lcc _cLE
998			_b04/2023 _dz _eIG _zSI