Differential Geometric Structures
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Differential Geometric Structures
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Author : Walter A. Poor
language : en
Publisher: Courier Corporation
Release Date : 2007-06-05
Differential Geometric Structures written by Walter A. Poor and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-06-05 with Mathematics categories.
Useful for independent study and as a reference work, this introduction to differential geometry features many examples and exercises. It defines geometric structure by specifying the parallel transport in an appropriate fiber bundle, focusing on the simplest cases of linear parallel transport in a vector bundle. The treatment opens with an introductory chapter on fiber bundles that proceeds to examinations of connection theory for vector bundles and Riemannian vector bundles. Additional topics include the role of harmonic theory, geometric vector fields on Riemannian manifolds, Lie groups, symmetric spaces, and symplectic and Hermitian vector bundles. A consideration of other differential geometric structures concludes the text, including surveys of characteristic classes of principal bundles, Cartan connections, and spin structures.
Modern Geometric Structures And Fields
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Author : Сергей Петрович Новиков
language : en
Publisher: American Mathematical Soc.
Release Date : 2006
Modern Geometric Structures And Fields written by Сергей Петрович Новиков 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 2006 with Mathematics categories.
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.
New Horizons In Differential Geometry And Its Related Fields
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Author : Toshiaki Adachi
language : en
Publisher: World Scientific
Release Date : 2022-04-07
New Horizons In Differential Geometry And Its Related Fields written by Toshiaki Adachi and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-04-07 with Mathematics categories.
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.
Transformation Groups In Differential Geometry
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Author : Shoshichi Kobayashi
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Transformation Groups In Differential Geometry written by Shoshichi Kobayashi 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.
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.
Differential Geometric Structures And Applications
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Author : Vladimir Rovenski
language : en
Publisher: Springer Nature
Release Date : 2024-03-15
Differential Geometric Structures And Applications written by Vladimir Rovenski and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-03-15 with Mathematics categories.
This proceedings contains a collection of selected, peer-reviewed contributions from the 4th International Workshop "Differential Geometric Structures and Applications" held in Haifa, Israel from May 10–13, 2023. The papers included in this volume showcase the latest advancements in modern geometry and interdisciplinary applications in fields ranging from mathematical physics to biology. Since 2008, this workshop series has provided a platform for researchers in pure and applied mathematics, including students, to engage in discussions and explore the frontiers of modern geometry. Previous workshops in the series have focused on topics such as "Reconstruction of Geometrical Objects Using Symbolic Computations" (2008), "Geometry and Symbolic Computations" (2013), and "Geometric Structures and Interdisciplinary Applications" (2018).
Foliations And Geometric Structures
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Author : Aurel Bejancu
language : en
Publisher: Springer
Release Date : 2010-11-19
Foliations And Geometric Structures written by Aurel Bejancu and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-11-19 with Mathematics categories.
This self-contained book starts with the basic material on distributions and foliations. It then gradually introduces and builds the tools needed for studying the geometry of foliated manifolds. The main theme of the book is to investigate the interrelations between foliations of a manifold on the one hand, and the many geometric structures that the manifold may admit on the other hand. Among these structures are: affine, Riemannian, semi-Riemannian, Finsler, symplectic, complex and contact structures. Using these structures, the book presents interesting classes of foliations whose geometry is very rich and promising. These include the classes of: Riemannian, totally geodesic, totally umbilical, minimal, parallel non-degenerate, parallel totally - null, parallel partially - null, symmetric, transversally symmetric, Lagrange, totally real and Legendre foliations. Some of these classes appear for the first time in the literature in book form. Finally, the vertical foliation of a vector bundle is used to develop a gauge theory on the total space of a vector bundle.
Geometric Structures Of Information
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Author : Frank Nielsen
language : en
Publisher: Springer
Release Date : 2018-11-29
Geometric Structures Of Information written by Frank Nielsen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-29 with Technology & Engineering categories.
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.
Manifolds And Differential Geometry
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Author : Jeffrey M. Lee
language : en
Publisher: American Mathematical Society
Release Date : 2022-03-08
Manifolds And Differential Geometry written by Jeffrey M. Lee and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-03-08 with Mathematics categories.
Differential geometry began as the study of curves and surfaces using the methods of calculus. In time, the notions of curve and surface were generalized along with associated notions such as length, volume, and curvature. At the same time the topic has become closely allied with developments in topology. The basic object is a smooth manifold, to which some extra structure has been attached, such as a Riemannian metric, a symplectic form, a distinguished group of symmetries, or a connection on the tangent bundle. This book is a graduate-level introduction to the tools and structures of modern differential geometry. Included are the topics usually found in a course on differentiable manifolds, such as vector bundles, tensors, differential forms, de Rham cohomology, the Frobenius theorem and basic Lie group theory. The book also contains material on the general theory of connections on vector bundles and an in-depth chapter on semi-Riemannian geometry that covers basic material about Riemannian manifolds and Lorentz manifolds. An unusual feature of the book is the inclusion of an early chapter on the differential geometry of hypersurfaces in Euclidean space. There is also a section that derives the exterior calculus version of Maxwell's equations. The first chapters of the book are suitable for a one-semester course on manifolds. There is more than enough material for a year-long course on manifolds and geometry.
Topological Differential And Conformal Geometry Of Surfaces
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Author : Norbert A'Campo
language : en
Publisher: Springer
Release Date : 2021-10-28
Topological Differential And Conformal Geometry Of Surfaces written by Norbert A'Campo and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-10-28 with Mathematics categories.
This book provides an introduction to the main geometric structures that are carried by compact surfaces, with an emphasis on the classical theory of Riemann surfaces. It first covers the prerequisites, including the basics of differential forms, the Poincaré Lemma, the Morse Lemma, the classification of compact connected oriented surfaces, Stokes’ Theorem, fixed point theorems and rigidity theorems. There is also a novel presentation of planar hyperbolic geometry. Moving on to more advanced concepts, it covers topics such as Riemannian metrics, the isometric torsion-free connection on vector fields, the Ansatz of Koszul, the Gauss–Bonnet Theorem, and integrability. These concepts are then used for the study of Riemann surfaces. One of the focal points is the Uniformization Theorem for compact surfaces, an elementary proof of which is given via a property of the energy functional. Among numerous other results, there is also a proof of Chow’s Theorem on compact holomorphic submanifolds in complex projective spaces. Based on lecture courses given by the author, the book will be accessible to undergraduates and graduates interested in the analytic theory of Riemann surfaces.