9783031012693 - the geometry of walker manifolds di gilkey, peter; brozos-vázquez, miguel; garcia-rio, eduardo; nikčević, stana; vásquez-lorenzo, ramón (11 risultati)
The Geometry of Walker Manifolds (Synthesis Lectures on Mathematics & Statistics)
Gilkey, Peter; Brozos-Vázquez, Miguel; Garcia-Rio, Eduardo; Nikčević, Stana; Vásquez-Lorenzo, Ramón
Lingua: Inglese
Editore: Springer, 2009
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The Geometry of Walker Manifolds (Synthesis Lectures on Mathematics & Statistics)
Gilkey, Peter; Brozos-Vázquez, Miguel; Garcia-Rio, Eduardo; Nikčević, Stana; Vásquez-Lorenzo, Ramón
Lingua: Inglese
Editore: Springer, 2009
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Lingua: Inglese
Editore: Springer, 2009
Serie: Libro 4 di 72 - Synthesis Lectures on Mathematics & Statistics
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Taschenbuch. Condizione: Neu. Druck auf Anfrage Neuware - Printed after ordering - This 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 s…ome 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.
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Lingua: Inglese
Editore: Springer, 2009
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Taschenbuch. Condizione: Neu. The Geometry of Walker Manifolds | Peter Gilkey (u. a.) | Taschenbuch | Synthesis Lectures on Mathematics & Statistics | xvii | Englisch | 2009 | Springer | EAN 9783031012693 | Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg, juergen[dot]hartmann[at]sprin…ger[dot]com | Anbieter: preigu.
Lingua: Inglese
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The Geometry of Walker Manifolds
Gilkey, Peter; Brozos-Vázquez, Miguel; Garcia-Rio, Eduardo; Nikčević, Stana; Vásquez-Lorenzo, Ramón
Lingua: Inglese
Editore: Springer, 2009
Serie: Libro 4 di 72 - Synthesis Lectures on Mathematics & Statistics
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The Geometry of Walker Manifolds (Synthesis Lectures on Mathematics & Statistics)
Gilkey, Peter; Brozos-Vázquez, Miguel; Garcia-Rio, Eduardo; Nikčević, Stana; Vásquez-Lorenzo, Ramón
Lingua: Inglese
Editore: Springer, 2009
Serie: Libro 4 di 72 - Synthesis Lectures on Mathematics & Statistics
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The Geometry of Walker Manifolds (Synthesis Lectures on Mathematics & Statistics)
Gilkey, Peter; Brozos-Vázquez, Miguel; Garcia-Rio, Eduardo; Nikčević, Stana; Vásquez-Lorenzo, Ramón
Lingua: Inglese
Editore: Springer, 2009
Serie: Libro 4 di 72 - Synthesis Lectures on Mathematics & Statistics
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Lingua: Inglese
Editore: Springer International Publishing Jun 2009, 2009
Serie: Libro 4 di 72 - Synthesis Lectures on Mathematics & Statistics
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Taschenbuch. Condizione: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -This 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 180 pp. Englisch.
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The Geometry of Walker Manifolds
Peter Gilkey|Miguel Brozos-Vázquez|Eduardo Garcia-Rio|Stana Nikcevic|Ramón Vásquez-Lorenzo
Lingua: Inglese
Editore: Springer International Publishing, 2009
Serie: Libro 4 di 72 - Synthesis Lectures on Mathematics & Statistics
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Condizione: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Peter Gilkey is a Professor of Mathematics and a member of the Institute of Theoretical Science at the University of Oregon (USA). He is a fellow of the American Mathematical Society and is a member of the editorial…board of Results in Mathematics, Differen.
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Lingua: Inglese
Editore: Springer, Springer Jun 2009, 2009
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Taschenbuch. Condizione: Neu. This item is printed on demand - Print on Demand Titel. Neuware -This 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 ManifoldsSpringer-Verlag KG, Sachsenplatz 4-6, 1201 Wien 180 pp. Englisch.
