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Author : Walter A. Poor
Publisher : Courier Corporation
Page : 352 pages
File Size : 42,6 Mb
Release : 2015-04-27
Category : Mathematics
ISBN : 9780486151915
This introductory text defines geometric structure by specifying parallel transport in an appropriate fiber bundle and focusing on simplest cases of linear parallel transport in a vector bundle. 1981 edition.
Author : Robert Hermann
Publisher : Math Science Press
Page : 363 pages
File Size : 52,6 Mb
Release : 1991
Category : Mathematics
ISBN : 0915692422
VOLUME 26 of INTERDISCIPLINARY MATHEMATICS, series expounding mathematical methodology in Physics & Engineering. TOPICS: Differential & Riemannian Geometry; Theories of Vorticity Dynamics, Einstein-Hilbert Gravitation, Colobeau-Rosinger Generalized Function Algebra, Deformations & Quantum Mechanics of Particles & Fields. Ultimate goal is to develop mathematical framework for reconciling Quantum Mechanics & concept of Point Particle. New ideas for researchers & students. Order: Math Sci Press, 53 Jordan Road, Brookline, MA 02146. (617) 738-0307.
Author : Сергей Петрович Новиков,Искандер Асанович Тайманов
Publisher : American Mathematical Soc.
Page : 658 pages
File Size : 51,5 Mb
Release : 2006
Category : Diffentiable manifolds
ISBN : 9780821839294
Presents the basics of Riemannian geometry in its modern form as geometry of differentiable manifolds and the important structures on them. This book shows that Riemannian geometry has a great influence to several fundamental areas of modern mathematics and its applications.
Author : Vladimir Rovenski
Publisher : Springer Nature
Page : 323 pages
File Size : 46,6 Mb
Release : 2024-05-23
Category : Electronic
ISBN : 9783031505867
Author : Toshiaki Adachi,Hideya Hashimoto
Publisher : World Scientific
Page : 257 pages
File Size : 55,6 Mb
Release : 2022-04-07
Category : Mathematics
ISBN : 9789811248115
This volume presents recent developments in geometric structures on Riemannian manifolds and their discretizations. With chapters written by recognized experts, these discussions focus on contact structures, Kähler structures, fiber bundle structures and Einstein metrics. It also contains works on the geometric approach on coding theory.For researchers and students, this volume forms an invaluable source to learn about these subjects that are not only in the field of differential geometry but also in other wide related areas. It promotes and deepens the study of geometric structures.
Author : Shoshichi Kobayashi
Publisher : Springer Science & Business Media
Page : 192 pages
File Size : 43,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642619816
Given a mathematical structure, one of the basic associated mathematical objects is its automorphism group. The object of this book is to give a biased account of automorphism groups of differential geometric struc tures. All geometric structures are not created equal; some are creations of ~ods while others are products of lesser human minds. Amongst the former, Riemannian and complex structures stand out for their beauty and wealth. A major portion of this book is therefore devoted to these two structures. Chapter I describes a general theory of automorphisms of geometric structures with emphasis on the question of when the automorphism group can be given a Lie group structure. Basic theorems in this regard are presented in §§ 3, 4 and 5. The concept of G-structure or that of pseudo-group structure enables us to treat most of the interesting geo metric structures in a unified manner. In § 8, we sketch the relationship between the two concepts. Chapter I is so arranged that the reader who is primarily interested in Riemannian, complex, conformal and projective structures can skip §§ 5, 6, 7 and 8. This chapter is partly based on lec tures I gave in Tokyo and Berkeley in 1965.
Author : Javier De Lucas Araujo,Cristina Sardon Munoz
Publisher : World Scientific
Page : 425 pages
File Size : 54,8 Mb
Release : 2020-01-22
Category : Mathematics
ISBN : 9781786346995
The book presents a comprehensive guide to the study of Lie systems from the fundamentals of differential geometry to the development of contemporary research topics. It embraces several basic topics on differential geometry and the study of geometric structures while developing known applications in the theory of Lie systems. The book also includes a brief exploration of the applications of Lie systems to superequations, discrete systems, and partial differential equations.Offering a complete overview from the topic's foundations to the present, this book is an ideal resource for Physics and Mathematics students, doctoral students and researchers.
Author : Adachi Toshiaki,Hashimoto Hideya
Publisher : World Scientific
Page : 224 pages
File Size : 52,6 Mb
Release : 2019-10-15
Category : Mathematics
ISBN : 9789811206702
This volume contains papers by the main participants in the meeting of the 6th International Colloquium on Differential Geometry and its Related Fields (ICDG2018).The volume consists of papers devoted to the study of recent topics in geometric structures on manifolds — which are related to complex analysis, symmetric spaces and surface theory — and also in discrete mathematics.Thus, it presents a broad overview of differential geometry and provides up-to-date information to researchers and young scientists in this field, and also to those working in the wide spectrum of mathematics.
Author : Ercüment H. Ortaçgil
Publisher : Oxford University Press
Page : 240 pages
File Size : 47,5 Mb
Release : 2018-06-28
Category : Mathematics
ISBN : 9780192554840
This book presents a new and innovative approach to Lie groups and differential geometry. Rather than compiling and reviewing the existing material on this classical subject, Professor Ortaçgil instead questions the foundations of the subject, and proposes a new direction. Aimed at the curious and courageous mathematician, this book aims to provoke further debate and inspire further development of this original research.
Author : William M. Goldman
Publisher : American Mathematical Society
Page : 494 pages
File Size : 52,7 Mb
Release : 2022-12-29
Category : Mathematics
ISBN : 9781470471033
The theory of geometric structures on manifolds which are locally modeled on a homogeneous space of a Lie group traces back to Charles Ehresmann in the 1930s, although many examples had been studied previously. Such locally homogeneous geometric structures are special cases of Cartan connections where the associated curvature vanishes. This theory received a big boost in the 1970s when W. Thurston put his geometrization program for 3-manifolds in this context. The subject of this book is more ambitious in scope. Unlike Thurston's eight 3-dimensional geometries, it covers structures which are not metric structures, such as affine and projective structures. This book describes the known examples in dimensions one, two and three. Each geometry has its own special features, which provide special tools in its study. Emphasis is given to the interrelationships between different geometries and how one kind of geometric structure induces structures modeled on a different geometry. Up to now, much of the literature has been somewhat inaccessible and the book collects many of the pieces into one unified work. This book focuses on several successful classification problems. Namely, fix a geometry in the sense of Klein and a topological manifold. Then the different ways of locally putting the geometry on the manifold lead to a “moduli space”. Often the moduli space carries a rich geometry of its own reflecting the model geometry. The book is self-contained and accessible to students who have taken first-year graduate courses in topology, smooth manifolds, differential geometry and Lie groups.
Author : Francisco J. Carreras,Olga Gil-Medrano,Antonio M. Naveira
Publisher : Springer
Page : 313 pages
File Size : 53,7 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540468585
This volume of proceedings contains selected and refereed articles - both surveys and original research articles - on geometric structures, global analysis, differential operators on manifolds, cohomology theories and other topics in differential geometry.
Author : Jochen Brüning,Matthias Staudacher
Publisher : Walter de Gruyter GmbH & Co KG
Page : 517 pages
File Size : 40,9 Mb
Release : 2018-04-09
Category : Mathematics
ISBN : 9783110452150
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 : Esteban Calviño-Louzao,Eduardo García-Río,Peter Gilkey,JeongHyeong Park,Ramón Vázquez-Lorenzo
Publisher : Morgan & Claypool Publishers
Page : 169 pages
File Size : 48,5 Mb
Release : 2019-04-18
Category : Mathematics
ISBN : 9781681735641
Book IV continues the discussion begun in the first three volumes. Although it is aimed at first-year graduate students, it is also intended to serve as a basic reference for people working in affine differential geometry. It also should be accessible to undergraduates interested in affine differential geometry. We are primarily concerned with the study of affine surfaces which are locally homogeneous. We discuss affine gradient Ricci solitons, affine Killing vector fields, and geodesic completeness. Opozda has classified the affine surface geometries which are locally homogeneous; we follow her classification. Up to isomorphism, there are two simply connected Lie groups of dimension 2. The translation group R2 is Abelian and the ???? + ?? group is non-Abelian. The first chapter presents foundational material. The second chapter deals with Type ?? surfaces. These are the left-invariant affine geometries on R2. Associating to each Type ?? surface the space of solutions to the quasi-Einstein equation corresponding to the eigenvalue ?? = -1 turns out to be a very powerful technique and plays a central role in our study as it links an analytic invariant with the underlying geometry of the surface. The third chapter deals with Type ?? surfaces; these are the left-invariant affine geometries on the ???? + ?? group. These geometries form a very rich family which is only partially understood. The only remaining homogeneous geometry is that of the sphere ??2. The fourth chapter presents relations between the geometry of an affine surface and the geometry of the cotangent bundle equipped with the neutral signature metric of the modified Riemannian extension.
Author : Frank Nielsen
Publisher : Springer
Page : 392 pages
File Size : 50,9 Mb
Release : 2018-11-19
Category : Technology & Engineering
ISBN : 9783030025205
This book focuses on information geometry manifolds of structured data/information and their advanced applications featuring new and fruitful interactions between several branches of science: information science, mathematics and physics. It addresses interrelations between different mathematical domains like shape spaces, probability/optimization & algorithms on manifolds, relational and discrete metric spaces, computational and Hessian information geometry, algebraic/infinite dimensional/Banach information manifolds, divergence geometry, tensor-valued morphology, optimal transport theory, manifold & topology learning, and applications like geometries of audio-processing, inverse problems and signal processing. The book collects the most important contributions to the conference GSI’2017 – Geometric Science of Information.
Author : Toshiaki Adachi
Publisher : World Scientific
Page : 256 pages
File Size : 54,8 Mb
Release : 2015-10-22
Category : Mathematics
ISBN : 9789814719780
"This volume contains contributions by the main participants of the 4th International Colloquium on Differential Geometry and its Related Fields (ICDG2014). These articles cover recent developments and are devoted mainly to the study of some geometric structures on manifolds and graphs. Readers will find a broad overview of differential geometry and its relationship to other fields in mathematics and physics."--