Differential Geometric Structures

Differential Geometric Structures
Title Differential Geometric Structures PDF eBook
Author Walter A. Poor
Publisher Courier Corporation
Pages 356
Release 2015-04-27
Genre Mathematics
ISBN 0486151913

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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.

Differential Geometric Structures and Applications

Differential Geometric Structures and Applications
Title Differential Geometric Structures and Applications PDF eBook
Author Vladimir Rovenski
Publisher Springer Nature
Pages 323
Release
Genre
ISBN 3031505867

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Modern Geometric Structures and Fields

Modern Geometric Structures and Fields
Title Modern Geometric Structures and Fields PDF eBook
Author Сергей Петрович Новиков
Publisher American Mathematical Soc.
Pages 658
Release 2006
Genre Mathematics
ISBN 0821839292

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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.

Differential Geometric Structures and Applications

Differential Geometric Structures and Applications
Title Differential Geometric Structures and Applications PDF eBook
Author Vladimir Rovenski
Publisher
Pages 0
Release 2024
Genre
ISBN 9783031505874

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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).

Geometry and Complexity Theory

Geometry and Complexity Theory
Title Geometry and Complexity Theory PDF eBook
Author J. M. Landsberg
Publisher Cambridge University Press
Pages 353
Release 2017-09-28
Genre Computers
ISBN 110819141X

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Two central problems in computer science are P vs NP and the complexity of matrix multiplication. The first is also a leading candidate for the greatest unsolved problem in mathematics. The second is of enormous practical and theoretical importance. Algebraic geometry and representation theory provide fertile ground for advancing work on these problems and others in complexity. This introduction to algebraic complexity theory for graduate students and researchers in computer science and mathematics features concrete examples that demonstrate the application of geometric techniques to real world problems. Written by a noted expert in the field, it offers numerous open questions to motivate future research. Complexity theory has rejuvenated classical geometric questions and brought different areas of mathematics together in new ways. This book will show the beautiful, interesting, and important questions that have arisen as a result.

Differential Topology and Geometry with Applications to Physics

Differential Topology and Geometry with Applications to Physics
Title Differential Topology and Geometry with Applications to Physics PDF eBook
Author Eduardo Nahmad-Achar
Publisher
Pages 0
Release 2018
Genre Geometry, Differential
ISBN 9780750320726

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"Differential geometry has encountered numerous applications in physics. More and more physical concepts can be understood as a direct consequence of geometric principles. The mathematical structure of Maxwell's electrodynamics, of the general theory of relativity, of string theory, and of gauge theories, to name but a few, are of a geometric nature. All of these disciplines require a curved space for the description of a system, and we require a mathematical formalism that can handle the dynamics in such spaces if we wish to go beyond a simple and superficial discussion of physical relationships. This formalism is precisely differential geometry. Even areas like thermodynamics and fluid mechanics greatly benefit from a differential geometric treatment. Not only in physics, but in important branches of mathematics has differential geometry effected important changes. Aimed at graduate students and requiring only linear algebra and differential and integral calculus, this book presents, in a concise and direct manner, the appropriate mathematical formalism and fundamentals of differential topology and differential geometry together with essential applications in many branches of physics." -- Prové de l'editor.

New Horizons In Differential Geometry And Its Related Fields

New Horizons In Differential Geometry And Its Related Fields
Title New Horizons In Differential Geometry And Its Related Fields PDF eBook
Author Toshiaki Adachi
Publisher World Scientific
Pages 257
Release 2022-04-07
Genre Mathematics
ISBN 9811248117

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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.