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Metric Affine Manifold
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Book Synopsis Metric Affine Manifold by : Aleks Kleyn
Download or read book Metric Affine Manifold written by Aleks Kleyn and published by Createspace Independent Pub. This book was released on 2013-03-21 with total page 38 pages. Available in PDF, EPUB and Kindle. Book excerpt: I tell about different mathematical tool that is important in general relativity. The text of the book includes definition of geometric object, concept of reference frame, geometry of metric affinne manifold. Using this concept I learn dynamics in general relativity. We call a manifold with torsion and nonmetricity the metric affine manifold. The nonmetricity leads to a difference between the auto parallel line and the extreme line, and to a change in the expression of the Frenet transport. The torsion leads to a change in the Killing equation. We also need to add a similar equation for the connection. The dynamics of a particle follows to the Frenet transport. The analysis of the Frenet transport leads to the concept of the Cartan connection which is compatible with the metric tensor. We need additional physical constraints to make a nonmetricity observable.
Book Synopsis Metric Affine Manifold (Russian Edition) by : Aleks Kleyn
Download or read book Metric Affine Manifold (Russian Edition) written by Aleks Kleyn and published by CreateSpace. This book was released on 2013-03-21 with total page 42 pages. Available in PDF, EPUB and Kindle. Book excerpt: I tell about different mathematical tool that is important in general relativity. The text of the book includes definition of geometric object, concept of reference frame, geometry of metric\hyph affinne manifold. Using this concept I learn dynamics in general relativity. We call a manifold with torsion and nonmetricity the metric\hyph affine manifold. The nonmetricity leads to a difference between the auto parallel line and the extreme line, and to a change in the expression of the Frenet transport. The torsion leads to a change in the Killing equation. We also need to add a similar equation for the connection. The dynamics of a particle follows to the Frenet transport. The analysis of the Frenet transport leads to the concept of the Cartan connection which is compatible with the metric tensor. We need additional physical constraints to make a nonmetricity observable.
Book Synopsis The Decomposition and Classification of Radiant Affine 3-Manifolds by : Suhyoung Choi
Download or read book The Decomposition and Classification of Radiant Affine 3-Manifolds written by Suhyoung Choi and published by American Mathematical Soc.. This book was released on 2001 with total page 137 pages. Available in PDF, EPUB and Kindle. Book excerpt: An affine manifold is a manifold with torsion-free flat affine connection - a geometric topologist would define it as a manifold with an atlas of charts to the affine space with affine transition functions. This title is an in-depth examination of the decomposition and classification of radiant affine 3-manifolds - affine manifolds of the type that have a holonomy group consisting of affine transformations fixing a common fixed point.
Book Synopsis Covariance and Gauge Invariance in Continuum Physics by : Lalaonirina R. Rakotomanana
Download or read book Covariance and Gauge Invariance in Continuum Physics written by Lalaonirina R. Rakotomanana and published by Springer. This book was released on 2018-07-04 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a Lagrangian approach model to formulate various fields of continuum physics, ranging from gradient continuum elasticity to relativistic gravito-electromagnetism. It extends the classical theories based on Riemann geometry to Riemann-Cartan geometry, and then describes non-homogeneous continuum and spacetime with torsion in Einstein-Cartan relativistic gravitation. It investigates two aspects of invariance of the Lagrangian: covariance of formulation following the method of Lovelock and Rund, and gauge invariance where the active diffeomorphism invariance is considered by using local Poincaré gauge theory according to the Utiyama method. Further, it develops various extensions of strain gradient continuum elasticity, relativistic gravitation and electromagnetism when the torsion field of the Riemann-Cartan continuum is not equal to zero. Lastly, it derives heterogeneous wave propagation equations within twisted and curved manifolds and proposes a relation between electromagnetic potential and torsion tensor.
Book Synopsis Manifolds and Lie Groups by : J. Hano
Download or read book Manifolds and Lie Groups written by J. Hano and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 465 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is the collection of papers dedicated to Yozo Matsushima on his 60th birthday, which took place on February 11, 1980. A conference in Geometry in honor of Professor Matsushima was held at the University of Notre Dame on May 14 and 15, 1980. Some of the papers in this volume were delivered on this occasion. 0 00 0\ - 15 S. Kobayashi, University 27 R. Ogawa, Loyola 42 P. Ryan, Indiana 1 W. Stoll 2 W. Kaup, University of of California at Berkeley University (Chicago) University at South Bend Tubing en 16 B.Y. Chen, 28 A. Howard 43 M. Kuga, SUNY at 3 G. Shimura, Michigan State University 29 D. Blair, Stony Brook Princeton University 17 G. Ludden, Michigan State University 44 W. Higgins 30 B. Smyth 4 A. Borel, Institute for Michigan State University 45 J. Curry Advanced Study 18 S. Harris, 31 A. Pradhan 46 D. Norris 32 R. Escobales, 5 Y. Matsushima University of Missouri 47 J. Spellecy Canisius College 6 Mrs. Matsushima 19 J. Beem, 48 M. Clancy 7 K. Nomizu, University of Missouri 33 L. Smiley 49 J. Rabinowitz, University 20 D. Collins, 34 C.H. Sung Brown University of Illinois at Chicago Valparaiso University 35 M. Markowitz 8 J.-1. Hano, 50 R. Richardson, Australian Washington University 36 A. Sommese 21 I. Satake, University of National University California at Berkeley 37 A. Vitter, 9 J. Carrell, University of 51 D. Lieberman, 22 H.
Book Synopsis Applications of Affine and Weyl Geometry by : Eduardo García-Río
Download or read book Applications of Affine and Weyl Geometry written by Eduardo García-Río and published by Morgan & Claypool Publishers. This book was released on 2013-05-01 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: Pseudo-Riemannian geometry is, to a large extent, the study of the Levi-Civita connection, which is the unique torsion-free connection compatible with the metric structure. There are, however, other affine connections which arise in different contexts, such as conformal geometry, contact structures, Weyl structures, and almost Hermitian geometry. In this book, we reverse this point of view and instead associate an auxiliary pseudo-Riemannian structure of neutral signature to certain affine connections and use this correspondence to study both geometries. We examine Walker structures, Riemannian extensions, and Kähler--Weyl geometry from this viewpoint. This book is intended to be accessible to mathematicians who are not expert in the subject and to students with a basic grounding in differential geometry. Consequently, the first chapter contains a comprehensive introduction to the basic results and definitions we shall need---proofs are included of many of these results to make it as self-contained as possible. Para-complex geometry plays an important role throughout the book and consequently is treated carefully in various chapters, as is the representation theory underlying various results. It is a feature of this book that, rather than as regarding para-complex geometry as an adjunct to complex geometry, instead, we shall often introduce the para-complex concepts first and only later pass to the complex setting. The second and third chapters are devoted to the study of various kinds of Riemannian extensions that associate to an affine structure on a manifold a corresponding metric of neutral signature on its cotangent bundle. These play a role in various questions involving the spectral geometry of the curvature operator and homogeneous connections on surfaces. The fourth chapter deals with Kähler--Weyl geometry, which lies, in a certain sense, midway between affine geometry and Kähler geometry. Another feature of the book is that we have tried wherever possible to find the original references in the subject for possible historical interest. Thus, we have cited the seminal papers of Levi-Civita, Ricci, Schouten, and Weyl, to name but a few exemplars. We have also given different proofs of various results than those that are given in the literature, to take advantage of the unified treatment of the area given herein.
Book Synopsis Applications of Affine and Weyl Geometry by : Eduardo García-Río
Download or read book Applications of Affine and Weyl Geometry written by Eduardo García-Río and published by Springer Nature. This book was released on 2022-05-31 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: Pseudo-Riemannian geometry is, to a large extent, the study of the Levi-Civita connection, which is the unique torsion-free connection compatible with the metric structure. There are, however, other affine connections which arise in different contexts, such as conformal geometry, contact structures, Weyl structures, and almost Hermitian geometry. In this book, we reverse this point of view and instead associate an auxiliary pseudo-Riemannian structure of neutral signature to certain affine connections and use this correspondence to study both geometries. We examine Walker structures, Riemannian extensions, and Kähler--Weyl geometry from this viewpoint. This book is intended to be accessible to mathematicians who are not expert in the subject and to students with a basic grounding in differential geometry. Consequently, the first chapter contains a comprehensive introduction to the basic results and definitions we shall need---proofs are included of many of these results to make it as self-contained as possible. Para-complex geometry plays an important role throughout the book and consequently is treated carefully in various chapters, as is the representation theory underlying various results. It is a feature of this book that, rather than as regarding para-complex geometry as an adjunct to complex geometry, instead, we shall often introduce the para-complex concepts first and only later pass to the complex setting. The second and third chapters are devoted to the study of various kinds of Riemannian extensions that associate to an affine structure on a manifold a corresponding metric of neutral signature on its cotangent bundle. These play a role in various questions involving the spectral geometry of the curvature operator and homogeneous connections on surfaces. The fourth chapter deals with Kähler--Weyl geometry, which lies, in a certain sense, midway between affine geometry and Kähler geometry. Another feature of the book is that we have tried wherever possible to find the original references in the subject for possible historical interest. Thus, we have cited the seminal papers of Levi-Civita, Ricci, Schouten, and Weyl, to name but a few exemplars. We have also given different proofs of various results than those that are given in the literature, to take advantage of the unified treatment of the area given herein.
Book Synopsis Harmonic Maps and Differential Geometry by : Eric Loubeau
Download or read book Harmonic Maps and Differential Geometry written by Eric Loubeau and published by American Mathematical Soc.. This book was released on 2011 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of a conference held in Cagliari, Italy, from September 7-10, 2009, to celebrate John C. Wood's 60th birthday. These papers reflect the many facets of the theory of harmonic maps and its links and connections with other topics in Differential and Riemannian Geometry. Two long reports, one on constant mean curvature surfaces by F. Pedit and the other on the construction of harmonic maps by J. C. Wood, open the proceedings. These are followed by a mix of surveys on Prof. Wood's area of expertise: Lagrangian surfaces, biharmonic maps, locally conformally Kahler manifolds and the DDVV conjecture, as well as several research papers on harmonic maps. Other research papers in the volume are devoted to Willmore surfaces, Goldstein-Pedrich flows, contact pairs, prescribed Ricci curvature, conformal fibrations, the Fadeev-Hopf model, the Compact Support Principle and the curvature of surfaces.
Book Synopsis On Manifolds with an Affine Connection and the Theory of General Relativity by : Elie Cartan
Download or read book On Manifolds with an Affine Connection and the Theory of General Relativity written by Elie Cartan and published by . This book was released on 1986 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Geometric Science of Information by : Frank Nielsen
Download or read book Geometric Science of Information written by Frank Nielsen and published by Springer. This book was released on 2019-08-19 with total page 764 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the proceedings of the 4th International Conference on Geometric Science of Information, GSI 2019, held in Toulouse, France, in August 2019. The 79 full papers presented in this volume were carefully reviewed and selected from 105 submissions. They cover all the main topics and highlights in the domain of geometric science of information, including information geometry manifolds of structured data/information and their advanced applications.
Book Synopsis Relativity and Geometry by : Roberto Torretti
Download or read book Relativity and Geometry written by Roberto Torretti and published by Elsevier. This book was released on 2014-05-20 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt: Relativity and Geometry aims to elucidate the motivation and significance of the changes in physical geometry brought about by Einstein, in both the first and the second phases of relativity. The book contains seven chapters and a mathematical appendix. The first two chapters review a historical background of relativity. Chapter 3 centers on Einstein's first Relativity paper of 1905. Subsequent chapter presents the Minkowskian formulation of special relativity. Chapters 5 and 6 deal with Einstein's search for general relativity from 1907 to 1915, as well as some aspects and subsequent developments of the theory. The last chapter explores the concept of simultaneity, geometric conventionalism, and a few other questions concerning space time structure, causality, and time.
Book Synopsis Extrinsic Geometry of Foliations by : Vladimir Rovenski
Download or read book Extrinsic Geometry of Foliations written by Vladimir Rovenski and published by Springer Nature. This book was released on 2021-05-22 with total page 319 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to geometric problems of foliation theory, in particular those related to extrinsic geometry, modern branch of Riemannian Geometry. The concept of mixed curvature is central to the discussion, and a version of the deep problem of the Ricci curvature for the case of mixed curvature of foliations is examined. The book is divided into five chapters that deal with integral and variation formulas and curvature and dynamics of foliations. Different approaches and methods (local and global, regular and singular) in solving the problems are described using integral and variation formulas, extrinsic geometric flows, generalizations of the Ricci and scalar curvatures, pseudo-Riemannian and metric-affine geometries, and 'computable' Finsler metrics. The book presents the state of the art in geometric and analytical theory of foliations as a continuation of the authors' life-long work in extrinsic geometry. It is designed for newcomers to the field as well as experienced geometers working in Riemannian geometry, foliation theory, differential topology, and a wide range of researchers in differential equations and their applications. It may also be a useful supplement to postgraduate level work and can inspire new interesting topics to explore.
Book Synopsis Contemporary Materialism: Its Ontology and Epistemology by : Gustavo E. Romero
Download or read book Contemporary Materialism: Its Ontology and Epistemology written by Gustavo E. Romero and published by Springer Nature. This book was released on 2022-06-01 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an up-to-date revision of materialism’s central tenets, its main varieties, and the place of materialistic philosophy vis a vis scientific knowledge. Materialism has been the subject of extensive and rich controversies since Robert Boyle introduced the term for the first time in the 17th century. But what is materialism and what can it offer today? The term is usually defined as the worldview according to which everything real is material. Nevertheless, there is no philosophical consensus about whether the meaning of matter can be enlarged beyond the physical. As a consequence, materialism is often defined in stark exclusive and reductionist terms: whatever exists is either physical or ontologically reducible to it. This conception, if consistent, mutilates reality, excluding the ontological significance of political, economic, sociocultural, anthropological and psychological realities. Starting from a new history of materialism, the present book focuses on the central ontological and epistemological debates aroused by today’s leading materialist approaches, including some little known to an anglophone readership. The key concepts of matter, system, emergence, space and time, life, mind, and software are checked over and updated. Controversial issues such as the nature of mathematics and the place of reductionism are also discussed from different materialist approaches. As a result, materialism emerges as a powerful, indispensable scientifically-supported worldview with a surprising wealth of nuances and possibilities.
Download or read book Geometry in History written by S. G. Dani and published by Springer Nature. This book was released on 2019-10-18 with total page 759 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a collection of surveys on important mathematical ideas, their origin, their evolution and their impact in current research. The authors are mathematicians who are leading experts in their fields. The book is addressed to all mathematicians, from undergraduate students to senior researchers, regardless of the specialty.
Book Synopsis Advances on Tensor Analysis and their Applications by : Francisco Bulnes
Download or read book Advances on Tensor Analysis and their Applications written by Francisco Bulnes and published by BoD – Books on Demand. This book was released on 2020-09-09 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book brings together recent advances in tensor analysis and studies of its invariants such as twistors, spinors, kinematic tensors and others belonging to tensor algebras with extended structures to Lie algebras, Kac-Moody algebras, and enveloping algebras, among others. Chapters cover such topics as classical tensors and bilinear forms, tensors for exploring space–time, tensor applications in geometry and continuum media, and advanced topics in tensor analysis such as invariant theory, derived categories, hypercohomologies, k-modules, extensions of kinematic tensors, infinite dimensional operators, and more.
Book Synopsis Dirichlet Branes and Mirror Symmetry by :
Download or read book Dirichlet Branes and Mirror Symmetry written by and published by American Mathematical Soc.. This book was released on 2009 with total page 698 pages. Available in PDF, EPUB and Kindle. Book excerpt: Research in string theory has generated a rich interaction with algebraic geometry, with exciting work that includes the Strominger-Yau-Zaslow conjecture. This monograph builds on lectures at the 2002 Clay School on Geometry and String Theory that sought to bridge the gap between the languages of string theory and algebraic geometry.
Book Synopsis Algebraic Geometry by : Dan Abramovich
Download or read book Algebraic Geometry written by Dan Abramovich and published by American Mathematical Soc.. This book was released on 2009 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains research and expository papers by some of the speakers at the 2005 AMS Summer Institute on Algebraic Geometry. Numerous papers delve into the geometry of various moduli spaces, including those of stable curves, stable maps, coherent sheaves, and abelian varieties.
