Curvature Of Space And Time With An Introduction To Geometric Analysis

Author : Iva Stavrov
Publisher : American Mathematical Soc.
Page : 243 pages
File Size : 48,9 Mb
Release : 2020-11-12
Category : Education
ISBN : 9781470456283

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Curvature of Space and Time, with an Introduction to Geometric Analysis by Iva Stavrov Pdf

This book introduces advanced undergraduates to Riemannian geometry and mathematical general relativity. The overall strategy of the book is to explain the concept of curvature via the Jacobi equation which, through discussion of tidal forces, further helps motivate the Einstein field equations. After addressing concepts in geometry such as metrics, covariant differentiation, tensor calculus and curvature, the book explains the mathematical framework for both special and general relativity. Relativistic concepts discussed include (initial value formulation of) the Einstein equations, stress-energy tensor, Schwarzschild space-time, ADM mass and geodesic incompleteness. The concluding chapters of the book introduce the reader to geometric analysis: original results of the author and her undergraduate student collaborators illustrate how methods of analysis and differential equations are used in addressing questions from geometry and relativity. The book is mostly self-contained and the reader is only expected to have a solid foundation in multivariable and vector calculus and linear algebra. The material in this book was first developed for the 2013 summer program in geometric analysis at the Park City Math Institute, and was recently modified and expanded to reflect the author's experience of teaching mathematical general relativity to advanced undergraduates at Lewis & Clark College.

Author : Jürgen Jost
Publisher : Springer
Page : 697 pages
File Size : 46,8 Mb
Release : 2017-10-13
Category : Mathematics
ISBN : 9783319618609

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Riemannian Geometry and Geometric Analysis by Jürgen Jost Pdf

This established reference work continues to provide its readers with a gateway to some of the most interesting developments in contemporary geometry. It offers insight into a wide range of topics, including fundamental concepts of Riemannian geometry, such as geodesics, connections and curvature; the basic models and tools of geometric analysis, such as harmonic functions, forms, mappings, eigenvalues, the Dirac operator and the heat flow method; as well as the most important variational principles of theoretical physics, such as Yang-Mills, Ginzburg-Landau or the nonlinear sigma model of quantum field theory. The present volume connects all these topics in a systematic geometric framework. At the same time, it equips the reader with the working tools of the field and enables her or him to delve into geometric research. The 7th edition has been systematically reorganized and updated. Almost no page has been left unchanged. It also includes new material, for instance on symplectic geometry, as well as the Bishop-Gromov volume growth theorem which elucidates the geometric role of Ricci curvature. From the reviews:“This book provides a very readable introduction to Riemannian geometry and geometric analysis... With the vast development of the mathematical subject of geometric analysis, the present textbook is most welcome.” Mathematical Reviews “For readers familiar with the basics of differential geometry and some acquaintance with modern analysis, the book is reasonably self-contained. The book succeeds very well in laying out the foundations of modern Riemannian geometry and geometric analysis. It introduces a number of key techniques and provides a representative overview of the field.” Monatshefte für Mathematik

Author : Jochen Brüning,Matthias Staudacher
Publisher : Walter de Gruyter GmbH & Co KG
Page : 517 pages
File Size : 44,7 Mb
Release : 2018-04-09
Category : Mathematics
ISBN : 9783110452150

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Space – Time – Matter by Jochen Brüning,Matthias Staudacher Pdf

This monograph describes some of the most interesting results obtained by the mathematicians and physicists collaborating in the CRC 647 "Space – Time – Matter", in the years 2005 - 2016. The work presented concerns the mathematical and physical foundations of string and quantum field theory as well as cosmology. Important topics are the spaces and metrics modelling the geometry of matter, and the evolution of these geometries. The partial differential equations governing such structures and their singularities, special solutions and stability properties are discussed in detail. Contents Introduction Algebraic K-theory, assembly maps, controlled algebra, and trace methods Lorentzian manifolds with special holonomy – Constructions and global properties Contributions to the spectral geometry of locally homogeneous spaces On conformally covariant differential operators and spectral theory of the holographic Laplacian Moduli and deformations Vector bundles in algebraic geometry and mathematical physics Dyson–Schwinger equations: Fix-point equations for quantum fields Hidden structure in the form factors ofN = 4 SYM On regulating the AdS superstring Constraints on CFT observables from the bootstrap program Simplifying amplitudes in Maxwell-Einstein and Yang-Mills-Einstein supergravities Yangian symmetry in maximally supersymmetric Yang-Mills theory Wave and Dirac equations on manifolds Geometric analysis on singular spaces Singularities and long-time behavior in nonlinear evolution equations and general relativity

Author : James J. Callahan
Publisher : Springer Science & Business Media
Page : 474 pages
File Size : 45,9 Mb
Release : 2000
Category : Computers
ISBN : 0387986413

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The Geometry of Spacetime by James J. Callahan Pdf

Hermann Minkowski recast special relativity as essentially a new geometric structure for spacetime. This book looks at the ideas of both Einstein and Minkowski, and then introduces the theory of frames, surfaces and intrinsic geometry, developing the main implications of Einstein's general relativity theory.

Author : Vicente Cortés,Klaus Kröncke,Jan Louis
Publisher : Springer
Page : 121 pages
File Size : 49,9 Mb
Release : 2018-12-05
Category : Mathematics
ISBN : 9783030011260

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Geometric Flows and the Geometry of Space-time by Vicente Cortés,Klaus Kröncke,Jan Louis Pdf

This book consists of two lecture notes on geometric flow equations (O. Schnürer) and Lorentzian geometry - holonomy, spinors and Cauchy Problems (H. Baum and T. Leistner) written by leading experts in these fields. It grew out of the summer school “Geometric flows and the geometry of space-time” held in Hamburg (2016) and provides an excellent introduction for students of mathematics and theoretical physics to important themes of current research in global analysis, differential geometry and mathematical physics

Author : Sean M. Carroll
Publisher : Cambridge University Press
Page : 529 pages
File Size : 46,9 Mb
Release : 2019-08-08
Category : Science
ISBN : 9781108488396

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Spacetime and Geometry by Sean M. Carroll Pdf

An accessible introductory textbook on general relativity, covering the theory's foundations, mathematical formalism and major applications.

Author : Fei Han,Xingwang Xu,Weiping Zhang
Publisher : World Scientific
Page : 220 pages
File Size : 52,7 Mb
Release : 2016-04-18
Category : Mathematics
ISBN : 9789813100565

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Geometric Analysis Around Scalar Curvatures by Fei Han,Xingwang Xu,Weiping Zhang Pdf

This volume contains three expanded lecture notes from the program Scalar Curvature in Manifold Topology and Conformal Geometry that was held at the Institute for Mathematical Sciences from 1 November to 31 December 2014. The first chapter surveys the recent developments on the fourth-order equations with negative exponent from geometric points of view such as positive mass theorem and uniqueness results. The next chapter deals with the recent important progress on several conjectures such as the existence of non-flat smooth hyper-surfaces and Serrin's over-determined problem. And the final chapter induces a new technique to handle the equation with critical index and the sign change coefficient as well as the negative index term. These topics will be of interest to those studying conformal geometry and geometric partial differential equations. Contents:Lectures on the Fourth-Order Q Curvature Equation (Fengbo Hang and Paul C Yang)An Introduction to the Finite and Infinite Dimensional Reduction Methods (Manuel del Pino and Juncheng Wei)Einstein Constraint Equations on Riemannian Manifolds (Quôc Anh Ngô) Readership: Advanced undergraduates, graduate students and researchers interested in the study of conformal geometry and geometric partial differential equations.

Author : Marcus Kriele
Publisher : Springer Science & Business Media
Page : 436 pages
File Size : 50,6 Mb
Release : 2003-07-01
Category : Science
ISBN : 9783540483540

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Spacetime by Marcus Kriele Pdf

One of the most of exciting aspects is the general relativity pred- tion of black holes and the Such Big Bang. predictions gained weight the theorems through Penrose. singularity pioneered In various by te- books on theorems general relativity singularity are and then presented used to that black holes exist and that the argue universe started with a To date what has big been is bang. a critical of what lacking analysis these theorems predict-’ We of really give a proof a typical singul- theorem and this ity use theorem to illustrate problems arising through the of possibilities violations" and "causality weak "shell very crossing These singularities". add to the problems weight of view that the point theorems alone singularity are not sufficient to the existence of predict physical singularities. The mathematical theme of the book In order to both solid gain a of and intuition understanding good for any mathematical theory, one,should to realise it as model of try a a fam- iar non-mathematical theories have had concept. Physical an especially the important on of and impact development mathematics, conversely various modern theories physical rather require sophisticated mathem- ics for their formulation. both and mathematics Today, physics are so that it is often difficult complex to master the theories in both very s- in the of jects. However, case differential pseudo-Riemannian geometry or the general relativity between and mathematics relationship physics is and it is therefore especially close, to from interd- possible profit an ciplinary approach.

Author : Lawrence C. Shepley,Richard Alfred Matzner
Publisher : Unknown
Page : 208 pages
File Size : 52,6 Mb
Release : 1982
Category : Mathematics
ISBN : UOM:39015017212344

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Spacetime and Geometry by Lawrence C. Shepley,Richard Alfred Matzner Pdf

Why is the universe so symmetrical? / Dennis Sciama -- Null congruences and Plebanski-Schild spaces / Ivor Robinson -- Linearization stability / Dieter Brill -- Nonlinear model field theories based on harmonic mappings / Charles W. Misner -- Gravitational fields in general relativity / Roy F. Kerr -- On the potential barriers surrounding the Schwarzschild black hole / S. Chandrasekhar -- The initial value problem and beyond / James W. York, Jr. and Tsvi Piran.

Author : Ivo Terek Couto,Alexandre Lymberopoulos
Publisher : CRC Press
Page : 351 pages
File Size : 42,6 Mb
Release : 2021-01-05
Category : Mathematics
ISBN : 9781000223347

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Introduction to Lorentz Geometry by Ivo Terek Couto,Alexandre Lymberopoulos Pdf

Lorentz Geometry is a very important intersection between Mathematics and Physics, being the mathematical language of General Relativity. Learning this type of geometry is the first step in properly understanding questions regarding the structure of the universe, such as: What is the shape of the universe? What is a spacetime? What is the relation between gravity and curvature? Why exactly is time treated in a different manner than other spatial dimensions? Introduction to Lorentz Geometry: Curves and Surfaces intends to provide the reader with the minimum mathematical background needed to pursue these very interesting questions, by presenting the classical theory of curves and surfaces in both Euclidean and Lorentzian ambient spaces simultaneously. Features: Over 300 exercises Suitable for senior undergraduates and graduates studying Mathematics and Physics Written in an accessible style without loss of precision or mathematical rigor Solution manual available on www.routledge.com/9780367468644

Author : Francesco Catoni,Dino Boccaletti,Roberto Cannata,Vincenzo Catoni,Enrico Nichelatti,Paolo Zampetti
Publisher : Springer Science & Business Media
Page : 256 pages
File Size : 50,6 Mb
Release : 2008-06-29
Category : Mathematics
ISBN : 9783764386146

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The Mathematics of Minkowski Space-Time by Francesco Catoni,Dino Boccaletti,Roberto Cannata,Vincenzo Catoni,Enrico Nichelatti,Paolo Zampetti Pdf

This book arose out of original research on the extension of well-established applications of complex numbers related to Euclidean geometry and to the space-time symmetry of two-dimensional Special Relativity. The system of hyperbolic numbers is extensively studied, and a plain exposition of space-time geometry and trigonometry is given. Commutative hypercomplex systems with four unities are studied and attention is drawn to their interesting properties.

Author : George Francis Rayner Ellis,Ruth M. Williams
Publisher : Clarendon Press
Page : 394 pages
File Size : 41,5 Mb
Release : 2000
Category : Mathematics
ISBN : 0198506562

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Flat and Curved Space-times by George Francis Rayner Ellis,Ruth M. Williams Pdf

This text explains special relativity and the basics of general relativity from a geometric viewpoint. Space-time geometry is emphasised throughout, and up-to-date information is provided on black holes, gravitational collapse, and cosmology.

Author : Daniel W. Stroock
Publisher : American Mathematical Soc.
Page : 290 pages
File Size : 43,8 Mb
Release : 2000
Category : Mathematics
ISBN : 9780821838396

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An Introduction to the Analysis of Paths on a Riemannian Manifold by Daniel W. Stroock Pdf

Hoping to make the text more accessible to readers not schooled in the probabalistic tradition, Stroock (affiliation unspecified) emphasizes the geometric over the stochastic analysis of differential manifolds. Chapters deconstruct Brownian paths, diffusions in Euclidean space, intrinsic and extrinsic Riemannian geometry, Bocher's identity, and the bundle of orthonormal frames. The volume humbly concludes with an "admission of defeat" in regard to recovering the Li-Yau basic differential inequality. Annotation copyrighted by Book News, Inc., Portland, OR.

Author : Theodore Frankel
Publisher : Courier Corporation
Page : 194 pages
File Size : 55,5 Mb
Release : 2013-04-10
Category : Science
ISBN : 9780486289151

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Gravitational Curvature by Theodore Frankel Pdf

This classic text and reference monograph applies modern differential geometry to general relativity. A brief mathematical introduction to gravitational curvature, it emphasizes the subject's geometric essence and stresses the global aspects of cosmology. Suitable for independent study as well as for courses in differential geometry, relativity, and cosmology. 1979 edition.

Author : Taha Sochi
Publisher : Lulu.com
Page : 198 pages
File Size : 42,5 Mb
Release : 2024-06-16
Category : Electronic
ISBN : 9781387103249

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Introduction to Differential Geometry of Space Curves and Surfaces by Taha Sochi Pdf