Curvature In Mathematics And Physics
DOWNLOAD
Download Curvature In Mathematics And Physics PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Curvature In Mathematics And Physics book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
Curvature In Mathematics And Physics
DOWNLOAD
Author : Shlomo Sternberg
language : en
Publisher: Courier Corporation
Release Date : 2013-04-17
Curvature In Mathematics And Physics written by Shlomo Sternberg and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Mathematics categories.
Expert treatment introduces semi-Riemannian geometry and its principal physical application, Einstein's theory of general relativity, using the Cartan exterior calculus as a principal tool. Prerequisites include linear algebra and advanced calculus. 2012 edition.
Geometric Realizations Of Curvature
DOWNLOAD
Author : Miguel Brozos-Vázquez
language : en
Publisher: World Scientific
Release Date : 2012
Geometric Realizations Of Curvature written by Miguel Brozos-Vázquez and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.
A central area of study in Differential Geometry is the examination of the relationship between the purely algebraic properties of the Riemann curvature tensor and the underlying geometric properties of the manifold. In this book, the findings of numerous investigations in this field of study are reviewed and presented in a clear, coherent form, including the latest developments and proofs. Even though many authors have worked in this area in recent years, many fundamental questions still remain unanswered. Many studies begin by first working purely algebraically and then later progressing onto the geometric setting and it has been found that many questions in differential geometry can be phrased as problems involving the geometric realization of curvature. Curvature decompositions are central to all investigations in this area. The authors present numerous results including the Singer Thorpe decomposition, the Bokan decomposition, the Nikcevic decomposition, the Tricerri Vanhecke decomposition, the Gray Hervella decomposition and the De Smedt decomposition. They then proceed to draw appropriate geometric conclusions from these decompositions. The book organizes, in one coherent volume, the results of research completed by many different investigators over the past 30 years. Complete proofs are given of results that are often only outlined in the original publications. Whereas the original results are usually in the positive definite (Riemannian setting), here the authors extend the results to the pseudo-Riemannian setting and then further, in a complex framework, to para-Hermitian geometry as well. In addition to that, new results are obtained as well, making this an ideal text for anyone wishing to further their knowledge of the science of curvature.
Differential Geometry
DOWNLOAD
Author : Clifford Henry Taubes
language : en
Publisher: OUP Oxford
Release Date : 2011-10-14
Differential Geometry written by Clifford Henry Taubes and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-10-14 with Mathematics categories.
Bundles, connections, metrics and curvature are the 'lingua franca' of modern differential geometry and theoretical physics. This book will supply a graduate student in mathematics or theoretical physics with the fundamentals of these objects. Many of the tools used in differential topology are introduced and the basic results about differentiable manifolds, smooth maps, differential forms, vector fields, Lie groups, and Grassmanians are all presented here. Other material covered includes the basic theorems about geodesics and Jacobi fields, the classification theorem for flat connections, the definition of characteristic classes, and also an introduction to complex and Kähler geometry. Differential Geometry uses many of the classical examples from, and applications of, the subjects it covers, in particular those where closed form expressions are available, to bring abstract ideas to life. Helpfully, proofs are offered for almost all assertions throughout. All of the introductory material is presented in full and this is the only such source with the classical examples presented in detail.
Curvature And Variational Modeling In Physics And Biophysics
DOWNLOAD
Author : Oscar J. Garay
language : en
Publisher: American Institute of Physics
Release Date : 2008-04-22
Curvature And Variational Modeling In Physics And Biophysics written by Oscar J. Garay and has been published by American Institute of Physics this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-04-22 with Mathematics categories.
The School was mainly addressed to young researchers coming from different disciplines with a common interest in variational problems defined by curvature energy functionals. Curves and surfaces obtained as critical points of these functionals are investigated from a theoretical and numerical point of view. Applications are shown in Geometry, Physics and Biophysics. An elementary background in Differential Geometry and Variational Calculus is assumed.
Regularity Theory For Mean Curvature Flow
DOWNLOAD
Author : Klaus Ecker
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Regularity Theory For Mean Curvature Flow written by Klaus Ecker and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
* Devoted to the motion of surfaces for which the normal velocity at every point is given by the mean curvature at that point; this geometric heat flow process is called mean curvature flow. * Mean curvature flow and related geometric evolution equations are important tools in mathematics and mathematical physics.
Symmetries And Curvature Structure In General Relativity
DOWNLOAD
Author : Hall Graham S
language : en
Publisher: World Scientific
Release Date : 2004-04-27
Symmetries And Curvature Structure In General Relativity written by Hall Graham S and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-04-27 with Science categories.
This is a text on classical general relativity from a geometrical viewpoint. Introductory chapters are provided on algebra, topology and manifold theory, together with a chapter on the basic ideas of space-time manifolds and Einstein's theory. There is a detailed account of algebraic structures and tensor classification in general relativity and also of the relationships between the metric, connection and curvature structures on space-times. The latter includes chapters on holonomy and sectional curvature. An extensive study is presented of symmetries in general relativity, including isometries, homotheties, conformal symmetries and affine, projective and curvature collineations. Several general properties of such symmetries are studied and a preparatory section on transformation groups and on the properties of Lie algebras of vector fields on manifolds is provided.
Gravitational Curvature
DOWNLOAD
Author : Theodore Frankel
language : en
Publisher: Courier Corporation
Release Date : 2013-04-10
Gravitational Curvature written by Theodore Frankel and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-10 with Science categories.
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.
Curvature Of Space And Time With An Introduction To Geometric Analysis
DOWNLOAD
Author : Iva Stavrov
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-11-12
Curvature Of Space And Time With An Introduction To Geometric Analysis written by Iva Stavrov and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-12 with Education categories.
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.
Flat And Curved Space Times
DOWNLOAD
Author : George Francis Rayner Ellis
language : en
Publisher: Clarendon Press
Release Date : 2000
Flat And Curved Space Times written by George Francis Rayner Ellis and has been published by Clarendon Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
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.
Differential Geometry
DOWNLOAD
Author : Clifford Henry Taubes
language : en
Publisher: OUP Oxford
Release Date : 2011-10-13
Differential Geometry written by Clifford Henry Taubes and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-10-13 with Mathematics categories.
Bundles, connections, metrics & curvature are the lingua franca of modern differential geometry & theoretical physics. Supplying graduate students in mathematics or theoretical physics with the fundamentals of these objects, & providing numerous examples, the book would suit a one-semester course on the subject of bundles & the associated geometry