Differential Geometry In The Large

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Differential Geometry in the Large

Author : Heinz Hopf
Publisher : Springer
ISBN 13 : 3540394826
Total Pages : 192 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Differential Geometry in the Large by : Heinz Hopf

Download or read book Differential Geometry in the Large written by Heinz Hopf and published by Springer. This book was released on 2003-07-01 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes consist of two parts: Selected in York 1) Geometry, New 1946, Topics University Notes Peter Lax. by Differential in the 2) Lectures on Stanford Geometry Large, 1956, Notes J.W. University by Gray. are here with no essential They reproduced change. Heinz was a mathematician who mathema- Hopf recognized important tical ideas and new mathematical cases. In the phenomena through special the central idea the of a or difficulty problem simplest background is becomes clear. in this fashion a crystal Doing geometry usually lead serious allows this to to - joy. Hopf's great insight approach for most of the in these notes have become the st- thematics, topics I will to mention a of further try ting-points important developments. few. It is clear from these notes that laid the on Hopf emphasis po- differential Most of the results in smooth differ- hedral geometry. whose is both t1al have understanding geometry polyhedral counterparts, works I wish to mention and recent important challenging. Among those of Robert on which is much in the Connelly rigidity, very spirit R. and in - of these notes (cf. Connelly, Conjectures questions open International of Mathematicians, H- of gidity, Proceedings Congress sinki vol. 1, 407-414) 1978, .

Differential Geometry in the Large

Author : Owen Dearricott
Publisher : Cambridge University Press
ISBN 13 : 1108879993
Total Pages : 402 pages
Book Rating : 4.1/5 (88 download)

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Book Synopsis Differential Geometry in the Large by : Owen Dearricott

Download or read book Differential Geometry in the Large written by Owen Dearricott and published by Cambridge University Press. This book was released on 2020-10-22 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 2019 'Australian-German Workshop on Differential Geometry in the Large' represented an extraordinary cross section of topics across differential geometry, geometric analysis and differential topology. The two-week programme featured talks from prominent keynote speakers from across the globe, treating geometric evolution equations, structures on manifolds, non-negative curvature and Alexandrov geometry, and topics in differential topology. A joy to the expert and novice alike, this proceedings volume touches on topics as diverse as Ricci and mean curvature flow, geometric invariant theory, Alexandrov spaces, almost formality, prescribed Ricci curvature, and Kähler and Sasaki geometry.

Differential Geometry in the Large

Author : Owen Dearricott
Publisher : Cambridge University Press
ISBN 13 : 1108812813
Total Pages : 401 pages
Book Rating : 4.1/5 (88 download)

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Book Synopsis Differential Geometry in the Large by : Owen Dearricott

Download or read book Differential Geometry in the Large written by Owen Dearricott and published by Cambridge University Press. This book was released on 2020-10-22 with total page 401 pages. Available in PDF, EPUB and Kindle. Book excerpt: From Ricci flow to GIT, physics to curvature bounds, Sasaki geometry to almost formality. This is differential geometry at large.

Differential Geometry

Author : J. J. Stoker
Publisher : John Wiley & Sons
ISBN 13 : 1118165470
Total Pages : 432 pages
Book Rating : 4.1/5 (181 download)

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Book Synopsis Differential Geometry by : J. J. Stoker

Download or read book Differential Geometry written by J. J. Stoker and published by John Wiley & Sons. This book was released on 2011-09-09 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: This classic work is now available in an unabridged paperback edition. Stoker makes this fertile branch of mathematics accessible to the nonspecialist by the use of three different notations: vector algebra and calculus, tensor calculus, and the notation devised by Cartan, which employs invariant differential forms as elements in an algebra due to Grassman, combined with an operation called exterior differentiation. Assumed are a passing acquaintance with linear algebra and the basic elements of analysis.

Differential Geometry

Author : Erwin Kreyszig
Publisher : Courier Corporation
ISBN 13 : 0486318621
Total Pages : 384 pages
Book Rating : 4.4/5 (863 download)

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Book Synopsis Differential Geometry by : Erwin Kreyszig

Download or read book Differential Geometry written by Erwin Kreyszig and published by Courier Corporation. This book was released on 2013-04-26 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introductory textbook on the differential geometry of curves and surfaces in 3-dimensional Euclidean space, presented in its simplest, most essential form. With problems and solutions. Includes 99 illustrations.

Manifolds and Differential Geometry

Author : Jeffrey M. Lee
Publisher : American Mathematical Society
ISBN 13 : 1470469820
Total Pages : 671 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Manifolds and Differential Geometry by : Jeffrey M. Lee

Download or read book Manifolds and Differential Geometry written by Jeffrey M. Lee and published by American Mathematical Society. This book was released on 2022-03-08 with total page 671 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Differential Geometry in the Large

Author :
Publisher :
ISBN 13 : 9780387120041
Total Pages : 0 pages
Book Rating : 4.1/5 (2 download)

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Book Synopsis Differential Geometry in the Large by :

Download or read book Differential Geometry in the Large written by and published by . This book was released on with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Real Analysis: A Comprehensive Course in Analysis, Part 1

Author : Barry Simon
Publisher : American Mathematical Soc.
ISBN 13 : 1470410990
Total Pages : 789 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Real Analysis: A Comprehensive Course in Analysis, Part 1 by : Barry Simon

Download or read book Real Analysis: A Comprehensive Course in Analysis, Part 1 written by Barry Simon and published by American Mathematical Soc.. This book was released on 2015-11-02 with total page 789 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Comprehensive Course in Analysis by Poincaré Prize winner Barry Simon is a five-volume set that can serve as a graduate-level analysis textbook with a lot of additional bonus information, including hundreds of problems and numerous notes that extend the text and provide important historical background. Depth and breadth of exposition make this set a valuable reference source for almost all areas of classical analysis. Part 1 is devoted to real analysis. From one point of view, it presents the infinitesimal calculus of the twentieth century with the ultimate integral calculus (measure theory) and the ultimate differential calculus (distribution theory). From another, it shows the triumph of abstract spaces: topological spaces, Banach and Hilbert spaces, measure spaces, Riesz spaces, Polish spaces, locally convex spaces, Fréchet spaces, Schwartz space, and spaces. Finally it is the study of big techniques, including the Fourier series and transform, dual spaces, the Baire category, fixed point theorems, probability ideas, and Hausdorff dimension. Applications include the constructions of nowhere differentiable functions, Brownian motion, space-filling curves, solutions of the moment problem, Haar measure, and equilibrium measures in potential theory.

Differential Geometry and Lie Groups for Physicists

Author : Marián Fecko
Publisher : Cambridge University Press
ISBN 13 : 1139458035
Total Pages : 11 pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Differential Geometry and Lie Groups for Physicists by : Marián Fecko

Download or read book Differential Geometry and Lie Groups for Physicists written by Marián Fecko and published by Cambridge University Press. This book was released on 2006-10-12 with total page 11 pages. Available in PDF, EPUB and Kindle. Book excerpt: Covering subjects including manifolds, tensor fields, spinors, and differential forms, this textbook introduces geometrical topics useful in modern theoretical physics and mathematics. It develops understanding through over 1000 short exercises, and is suitable for advanced undergraduate or graduate courses in physics, mathematics and engineering.

Geodesics and Curvature in Differential Geometry in the Large

Author : Harry Ernest Rauch
Publisher :
ISBN 13 :
Total Pages : 70 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis Geodesics and Curvature in Differential Geometry in the Large by : Harry Ernest Rauch

Download or read book Geodesics and Curvature in Differential Geometry in the Large written by Harry Ernest Rauch and published by . This book was released on 1959 with total page 70 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Differential Geometry in Physics

Author : Gabriel Lugo
Publisher :
ISBN 13 : 9781469669243
Total Pages : 372 pages
Book Rating : 4.6/5 (692 download)

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Book Synopsis Differential Geometry in Physics by : Gabriel Lugo

Download or read book Differential Geometry in Physics written by Gabriel Lugo and published by . This book was released on 2021-10-15 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential Geometry in Physics is a treatment of the mathematical foundations of the theory of general relativity and gauge theory of quantum fields. The material is intended to help bridge the gap that often exists between theoretical physics and applied mathematics. The approach is to carve an optimal path to learning this challenging field by appealing to the much more accessible theory of curves and surfaces. The transition from classical differential geometry as developed by Gauss, Riemann and other giants, to the modern approach, is facilitated by a very intuitive approach that sacrifices some mathematical rigor for the sake of understanding the physics. The book features numerous examples of beautiful curves and surfaces often reflected in nature, plus more advanced computations of trajectory of particles in black holes. Also embedded in the later chapters is a detailed description of the famous Dirac monopole and instantons. Features of this book: * Chapters 1-4 and chapter 5 comprise the content of a one-semester course taught by the author for many years. * The material in the other chapters has served as the foundation for many master's thesis at University of North Carolina Wilmington for students seeking doctoral degrees. * An open access ebook edition is available at Open UNC (https: //openunc.org) * The book contains over 80 illustrations, including a large array of surfaces related to the theory of soliton waves that does not commonly appear in standard mathematical texts on differential geometry.

Discrete Differential Geometry

Author : Alexander I. Bobenko
Publisher : American Mathematical Society
ISBN 13 : 1470474565
Total Pages : 432 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Discrete Differential Geometry by : Alexander I. Bobenko

Download or read book Discrete Differential Geometry written by Alexander I. Bobenko and published by American Mathematical Society. This book was released on 2023-09-14 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: An emerging field of discrete differential geometry aims at the development of discrete equivalents of notions and methods of classical differential geometry. The latter appears as a limit of a refinement of the discretization. Current interest in discrete differential geometry derives not only from its importance in pure mathematics but also from its applications in computer graphics, theoretical physics, architecture, and numerics. Rather unexpectedly, the very basic structures of discrete differential geometry turn out to be related to the theory of integrable systems. One of the main goals of this book is to reveal this integrable structure of discrete differential geometry. For a given smooth geometry one can suggest many different discretizations. Which one is the best? This book answers this question by providing fundamental discretization principles and applying them to numerous concrete problems. It turns out that intelligent theoretical discretizations are distinguished also by their good performance in applications. The intended audience of this book is threefold. It is a textbook on discrete differential geometry and integrable systems suitable for a one semester graduate course. On the other hand, it is addressed to specialists in geometry and mathematical physics. It reflects the recent progress in discrete differential geometry and contains many original results. The third group of readers at which this book is targeted is formed by specialists in geometry processing, computer graphics, architectural design, numerical simulations, and animation. They may find here answers to the question “How do we discretize differential geometry?” arising in their specific field. Prerequisites for reading this book include standard undergraduate background (calculus and linear algebra). No knowledge of differential geometry is expected, although some familiarity with curves and surfaces can be helpful.

Differential Geometry and Topology

Author : Keith Burns
Publisher : CRC Press
ISBN 13 : 1420057537
Total Pages : 400 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Differential Geometry and Topology by : Keith Burns

Download or read book Differential Geometry and Topology written by Keith Burns and published by CRC Press. This book was released on 2005-05-27 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: Accessible, concise, and self-contained, this book offers an outstanding introduction to three related subjects: differential geometry, differential topology, and dynamical systems. Topics of special interest addressed in the book include Brouwer's fixed point theorem, Morse Theory, and the geodesic flow. Smooth manifolds, Riemannian metrics, affine connections, the curvature tensor, differential forms, and integration on manifolds provide the foundation for many applications in dynamical systems and mechanics. The authors also discuss the Gauss-Bonnet theorem and its implications in non-Euclidean geometry models. The differential topology aspect of the book centers on classical, transversality theory, Sard's theorem, intersection theory, and fixed-point theorems. The construction of the de Rham cohomology builds further arguments for the strong connection between the differential structure and the topological structure. It also furnishes some of the tools necessary for a complete understanding of the Morse theory. These discussions are followed by an introduction to the theory of hyperbolic systems, with emphasis on the quintessential role of the geodesic flow. The integration of geometric theory, topological theory, and concrete applications to dynamical systems set this book apart. With clean, clear prose and effective examples, the authors' intuitive approach creates a treatment that is comprehensible to relative beginners, yet rigorous enough for those with more background and experience in the field.

Applied Differential Geometry

Author : William L. Burke
Publisher : Cambridge University Press
ISBN 13 : 9780521269292
Total Pages : 440 pages
Book Rating : 4.2/5 (692 download)

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Book Synopsis Applied Differential Geometry by : William L. Burke

Download or read book Applied Differential Geometry written by William L. Burke and published by Cambridge University Press. This book was released on 1985-05-31 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a self-contained introductory textbook on the calculus of differential forms and modern differential geometry. The intended audience is physicists, so the author emphasises applications and geometrical reasoning in order to give results and concepts a precise but intuitive meaning without getting bogged down in analysis. The large number of diagrams helps elucidate the fundamental ideas. Mathematical topics covered include differentiable manifolds, differential forms and twisted forms, the Hodge star operator, exterior differential systems and symplectic geometry. All of the mathematics is motivated and illustrated by useful physical examples.

Lectures on Differential Geometry in the Large

Author : Heinz Hopf
Publisher :
ISBN 13 :
Total Pages : 324 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis Lectures on Differential Geometry in the Large by : Heinz Hopf

Download or read book Lectures on Differential Geometry in the Large written by Heinz Hopf and published by . This book was released on 1956 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Differential and Riemannian Geometry

Author : Detlef Laugwitz
Publisher : Academic Press
ISBN 13 : 1483263983
Total Pages : 250 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Differential and Riemannian Geometry by : Detlef Laugwitz

Download or read book Differential and Riemannian Geometry written by Detlef Laugwitz and published by Academic Press. This book was released on 2014-05-12 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential and Riemannian Geometry focuses on the methodologies, calculations, applications, and approaches involved in differential and Riemannian geometry. The book first offers information on local differential geometry of space curves and surfaces and tensor calculus and Riemannian geometry. Discussions focus on tensor algebra and analysis, concept of a differentiable manifold, geometry of a space with affine connection, intrinsic geometry of surfaces, curvature of surfaces, and surfaces and curves on surfaces. The manuscript then examines further development and applications of Riemannian geometry and selections from differential geometry in the large, including curves and surfaces in the large, spaces of constant curvature and non-Euclidean geometry, Riemannian spaces and analytical dynamics, and metric differential geometry and characterizations of Riemannian geometry. The publication elaborates on prerequisite theorems of analysis, as well as the existence and uniqueness theorem for ordinary first-order differential equations and systems of equations and integrability theory for systems of first-order partial differential equations. The book is a valuable reference for researchers interested in differential and Riemannian geometry.

Differential Geometry of Curves and Surfaces

Author : Victor Andreevich Toponogov
Publisher : Springer Science & Business Media
ISBN 13 : 0817644024
Total Pages : 215 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis Differential Geometry of Curves and Surfaces by : Victor Andreevich Toponogov

Download or read book Differential Geometry of Curves and Surfaces written by Victor Andreevich Toponogov and published by Springer Science & Business Media. This book was released on 2006-09-10 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt: Central topics covered include curves, surfaces, geodesics, intrinsic geometry, and the Alexandrov global angle comparision theorem Many nontrivial and original problems (some with hints and solutions) Standard theoretical material is combined with more difficult theorems and complex problems, while maintaining a clear distinction between the two levels