DMCA. Copyrighted Work that you can Claim.
Base have 60 497 books.
Search:

# ðŸ“™ The Geometry of Walker Manifolds by Eduardo GarcÃ­a-RÃ­o, Miguel Brozos-VÃ¡zquez, RÃ¡mon VÃ¡zquez-Lorenzo, Stana Nikcevic â€” free pdf

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. 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

• File size: 1 545 604
• Format: pdf

Security code:

## Similar books results

Topology and Geometry of Manifolds: 2001 Georgia International Topology Conference, May 21-June 2, 2001, University of Georgia, Athens, Georgia free download by Gordana Matic, Clint McCrory (ed.)

Since 1961, the Georgia Topology Conference has been held every eight years to discuss the newest developments in topology. The goals of the conference are to disseminate new and important results and to encourage interaction among topologists who are in ...

Synthetic Geometry of Manifolds pdf free by Anders Kock

An elegant book that is sure to become the standard introduction to synthetic differential geometry....

Mathematical Methods of Classical Mechanics free download by V. I. Arnold, A. Weinstein, K. Vogtmann

In this text, the author constructs the mathematical apparatus of classical mechanics from the beginning, examining all the basic problems in dynamics, including the theory of oscillations, the theory of rigid body motion, and the Hamiltonian formalism....

Introduction to tensor analysis and the calculus of moving surfaces free pdf by Pavel Grinfeld (auth.)

This textbook is distinguished from other texts on the subject by the depth of the presentation and the discussion of the calculus of moving surfaces, which is an extension of tensor calculus to deforming manifolds.Designed for advanced undergraduate and ...

Geometry and Topology of Manifolds (Fields Institute Communications) download pdf by Hans U. Boden, Ian Hambleton, Andrew J. Nicas, B. Doug Park

This book contains expository papers that give an up-to-date account of recent developments and open problems in the geometry and topology of manifolds, along with several research articles that present new results appearing in published form for the firs...

Conformal Geometry of Discrete Groups and Manifolds free pdf by B. N. Apanasov

This book presents the first systematic account of conformal geometry of n-manifolds, as well as its Riemannian counterparts. A unifying theme is their discrete holonomy groups. In particular, hyperbolic manifolds, in dimension 3 and higher, are addres...

The geometry and topology of three-manifolds free download by William P Thurston

This is an electronic edition of the 1980 lecture notes distributed by Princeton University. The text was typed in TeX by Sheila Newbery, who also scanned the figures. Typos have been corrected (and probably others introduced), but otherwise no attempt ha...

Einstein Manifolds free pdf by Besse A.L.

Einstein's equations stem from General Relativity. In the context of Riemannian manifolds, an independent mathematical theory has developed around them. Recently, it has produced several striking results, which have been of great interest also to physicis...

This edition of the invaluable text Modern Differential Geometry for Physicists contains an additional chapter that introduces some of the basic ideas of general topology needed in differential geometry. A number of small corrections and additions have al...

Principles of adaptive optics pdf free by Robert Tyson

Since the publication of the second edition of Principles of Adaptive Optics, the developments and applications in this area have increased tremendously. Observatories are now producing outstanding science through adaptive optics technology; components, s...

Modelling and Dimensioning of Mobile Wireless Networks: From GSM to LTE download pdf by Maciej Stasiak, Mariusz Glabowski, Arkadiusz Wisniewski, Piotr Zwierzykowski

This book is a must-read for all network planners and other professionals wishing to improve the quality and cost efficiency of 3G and LTE networksIn this book, the authors address the architecture of the 2/3G network and the Long Term Evolution (LTE) net...

L'Anneau-Monde free pdf by Larry Niven

The Cambridge Companion to Greek and Roman Philosophy (Cambridge Companions to Philosophy) free pdf by David Sedley

This wide-ranging introduction to the study of philosophy in the ancient world surveys the period's developments and evaluates a comprehensive series of major thinkers, ranging from Pythagoras to Epicurus. Tables, illustrations, and extensive advice on fu...