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.
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.
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.
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.
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.
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.
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.
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:
Download or read book Global Affine Differential Geometry of Hypersurfaces written by An-Min Li and published by Walter de Gruyter GmbH & Co KG. This book was released on 2015-08-17 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book draws a colorful and widespread picture of global affine hypersurface theory up to the most recent state. Moreover, the recent development revealed that affine differential geometry – as differential geometry in general – has an exciting intersection area with other fields of interest, like partial differential equations, global analysis, convex geometry and Riemann surfaces. The second edition of this monograph leads the reader from introductory concepts to recent research. Since the publication of the first edition in 1993 there appeared important new contributions, like the solutions of two different affine Bernstein conjectures, due to Chern and Calabi, respectively. Moreover, a large subclass of hyperbolic affine spheres were classified in recent years, namely the locally strongly convex Blaschke hypersurfaces that have parallel cubic form with respect to the Levi-Civita connection of the Blaschke metric. The authors of this book present such results and new methods of proof.
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.
Download or read book Affine Flows on 3 Manifolds written by Shigenori Matsumoto and published by American Mathematical Soc.. This book was released on 2003 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt: Considers nonsingular flows on closed 3-manifolds which are transversely modeled on the real affine geometry of the plane. This book obtains classification results for three types of flows.
Download or read book Geometry of Submanifolds and Applications written by Bang-Yen Chen and published by Springer Nature. This book was released on with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Topology and Geometry of Manifolds written by Gordana Matic and published by American Mathematical Soc.. This book was released on 2003 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 different stages of their careers. Invited speakers are encouraged to aim their talks to a broad audience, and several talks are organized to introduce graduate students to topics of current interest. Each conference results in high-quality surveys, new research, and lists of unsolved problems, some of which are then formally published. Continuing in this 40-year tradition, the AMS presents this volume of articles and problem lists from the 2001 conference. Topics covered include symplectic and contact topology, foliations and laminations, and invariants of manifolds and knots. Articles of particular interest include John Etnyre's, ``Introductory Lectures on Contact Geometry'', which is a beautiful expository paper that explains the background and setting for many of the other papers. This is an excellent introduction to the subject for graduate students in neighboring fields. Etnyre and Lenhard Ng's, ``Problems in Low-Dimensional Contact Topology'' and Danny Calegari's extensive paper,``Problems in Foliations and Laminations of 3-Manifolds'' are carefully selected problems in keeping with the tradition of the conference. They were compiled by Etnyre and Ng and by Calegari with the input of many who were present. This book provides material of current interest to graduate students and research mathematicians interested in the geometry and topology of manifolds.
Download or read book An Introduction to Extremal Kahler Metrics written by Gábor Székelyhidi and published by American Mathematical Soc.. This book was released on 2014-06-19 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: A basic problem in differential geometry is to find canonical metrics on manifolds. The best known example of this is the classical uniformization theorem for Riemann surfaces. Extremal metrics were introduced by Calabi as an attempt at finding a higher-dimensional generalization of this result, in the setting of Kähler geometry. This book gives an introduction to the study of extremal Kähler metrics and in particular to the conjectural picture relating the existence of extremal metrics on projective manifolds to the stability of the underlying manifold in the sense of algebraic geometry. The book addresses some of the basic ideas on both the analytic and the algebraic sides of this picture. An overview is given of much of the necessary background material, such as basic Kähler geometry, moment maps, and geometric invariant theory. Beyond the basic definitions and properties of extremal metrics, several highlights of the theory are discussed at a level accessible to graduate students: Yau's theorem on the existence of Kähler-Einstein metrics, the Bergman kernel expansion due to Tian, Donaldson's lower bound for the Calabi energy, and Arezzo-Pacard's existence theorem for constant scalar curvature Kähler metrics on blow-ups.
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.
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.
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.
