New Problems In Differential Geometry

Author : Willi-Hans Steeb
Publisher : World Scientific Publishing Company
Page : 296 pages
File Size : 53,5 Mb
Release : 2017-10-20
Category : Mathematics
ISBN : 9789813230842

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Problems and Solutions in Differential Geometry, Lie Series, Differential Forms, Relativity and Applications by Willi-Hans Steeb Pdf

This volume presents a collection of problems and solutions in differential geometry with applications. Both introductory and advanced topics are introduced in an easy-to-digest manner, with the materials of the volume being self-contained. In particular, curves, surfaces, Riemannian and pseudo-Riemannian manifolds, Hodge duality operator, vector fields and Lie series, differential forms, matrix-valued differential forms, Maurer–Cartan form, and the Lie derivative are covered. Readers will find useful applications to special and general relativity, Yang–Mills theory, hydrodynamics and field theory. Besides the solved problems, each chapter contains stimulating supplementary problems and software implementations are also included. The volume will not only benefit students in mathematics, applied mathematics and theoretical physics, but also researchers in the field of differential geometry. Request Inspection Copy

Author : M. Rahula
Publisher : World Scientific
Page : 200 pages
File Size : 51,5 Mb
Release : 1993
Category : Mathematics
ISBN : 9810208197

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New Problems in Differential Geometry by M. Rahula Pdf

The main theme of this book is the geometrical interpretation of phenomena taking place in Jet spaces in connection with differential equations. This concise volume caters to all mathematicians who wish to deepen their acquaintance with the mathematics of differential geometry.

Author : A. T. Fomenko,A. S. Mishchenko,Yu. P. Solovyev
Publisher : Unknown
Page : 0 pages
File Size : 52,8 Mb
Release : 2013
Category : Geometry, Differential
ISBN : 1904868339

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Selected Problems in Differential Geometry and Topology by A. T. Fomenko,A. S. Mishchenko,Yu. P. Solovyev Pdf

This volume is a companion volume to A Short Course in Differential Geometry and Topology and is based on seminars held at Faculty of Mechanics and Mathematics at Moscow State University. It is intended as a supplementary text for graduate courses in differential geometry and topology. Parts 1 and 2 consist of problems and there are answers and solutions given.

Author : Mikio Nakahara
Publisher : Taylor & Francis
Page : 596 pages
File Size : 41,7 Mb
Release : 2018-10-03
Category : Mathematics
ISBN : 9781420056945

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Geometry, Topology and Physics by Mikio Nakahara Pdf

Differential geometry and topology have become essential tools for many theoretical physicists. In particular, they are indispensable in theoretical studies of condensed matter physics, gravity, and particle physics. Geometry, Topology and Physics, Second Edition introduces the ideas and techniques of differential geometry and topology at a level suitable for postgraduate students and researchers in these fields. The second edition of this popular and established text incorporates a number of changes designed to meet the needs of the reader and reflect the development of the subject. The book features a considerably expanded first chapter, reviewing aspects of path integral quantization and gauge theories. Chapter 2 introduces the mathematical concepts of maps, vector spaces, and topology. The following chapters focus on more elaborate concepts in geometry and topology and discuss the application of these concepts to liquid crystals, superfluid helium, general relativity, and bosonic string theory. Later chapters unify geometry and topology, exploring fiber bundles, characteristic classes, and index theorems. New to this second edition is the proof of the index theorem in terms of supersymmetric quantum mechanics. The final two chapters are devoted to the most fascinating applications of geometry and topology in contemporary physics, namely the study of anomalies in gauge field theories and the analysis of Polakov's bosonic string theory from the geometrical point of view. Geometry, Topology and Physics, Second Edition is an ideal introduction to differential geometry and topology for postgraduate students and researchers in theoretical and mathematical physics.

Author : Maido Rahula
Publisher : Unknown
Page : 192 pages
File Size : 46,9 Mb
Release : 1993
Category : Electronic
ISBN : 9812815422

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New Problems in Differential Geometry by Maido Rahula Pdf

Author : Owen Dearricott,Wilderich Tuschmann,Yuri Nikolayevsky,Diarmuid Crowley,Thomas Leistner
Publisher : Cambridge University Press
Page : 401 pages
File Size : 53,7 Mb
Release : 2020-10-22
Category : Mathematics
ISBN : 9781108812818

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Differential Geometry in the Large by Owen Dearricott,Wilderich Tuschmann,Yuri Nikolayevsky,Diarmuid Crowley,Thomas Leistner Pdf

From Ricci flow to GIT, physics to curvature bounds, Sasaki geometry to almost formality. This is differential geometry at large.

Author : Thierry Aubin
Publisher : American Mathematical Soc.
Page : 198 pages
File Size : 48,5 Mb
Release : 2001
Category : Geometry, Differential
ISBN : 9780821827093

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A Course in Differential Geometry by Thierry Aubin Pdf

This textbook for second-year graduate students is intended as an introduction to differential geometry with principal emphasis on Riemannian geometry. Chapter I explains basic definitions and gives the proofs of the important theorems of Whitney and Sard. Chapter II deals with vector fields and differential forms. Chapter III addresses integration of vector fields and p-plane fields. Chapter IV develops the notion of connection on a Riemannian manifold considered as a means to define parallel transport on the manifold. The author also discusses related notions of torsion and curvature, and gives a working knowledge of the covariant derivative. Chapter V specializes on Riemannian manifolds by deducing global properties from local properties of curvature, the final goal being to determine the manifold completely. Chapter VI explores some problems in PDEs suggested by the geometry of manifolds. The author is well-known for his significant contributions to the field of geometry and PDEs - particularly for his work on the Yamabe problem - and for his expository accounts on the subject. The text contains many problems and solutions, permitting the reader to apply the theorems and to see concrete developments of the abstract theory.

Author : R. W. R. Darling
Publisher : Cambridge University Press
Page : 288 pages
File Size : 52,7 Mb
Release : 1994-09-22
Category : Mathematics
ISBN : 0521468000

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Differential Forms and Connections by R. W. R. Darling Pdf

Introducing the tools of modern differential geometry--exterior calculus, manifolds, vector bundles, connections--this textbook covers both classical surface theory, the modern theory of connections, and curvature. With no knowledge of topology assumed, the only prerequisites are multivariate calculus and linear algebra.

Author : P.M. Gadea,J. Muñoz Masqué
Publisher : Springer Science & Business Media
Page : 478 pages
File Size : 52,8 Mb
Release : 2009-12-12
Category : Mathematics
ISBN : 9789048135646

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Analysis and Algebra on Differentiable Manifolds: A Workbook for Students and Teachers by P.M. Gadea,J. Muñoz Masqué Pdf

A famous Swiss professor gave a student’s course in Basel on Riemann surfaces. After a couple of lectures, a student asked him, “Professor, you have as yet not given an exact de nition of a Riemann surface.” The professor answered, “With Riemann surfaces, the main thing is to UNDERSTAND them, not to de ne them.” The student’s objection was reasonable. From a formal viewpoint, it is of course necessary to start as soon as possible with strict de nitions, but the professor’s - swer also has a substantial background. The pure de nition of a Riemann surface— as a complex 1-dimensional complex analytic manifold—contributes little to a true understanding. It takes a long time to really be familiar with what a Riemann s- face is. This example is typical for the objects of global analysis—manifolds with str- tures. There are complex concrete de nitions but these do not automatically explain what they really are, what we can do with them, which operations they really admit, how rigid they are. Hence, there arises the natural question—how to attain a deeper understanding? One well-known way to gain an understanding is through underpinning the d- nitions, theorems and constructions with hierarchies of examples, counterexamples and exercises. Their choice, construction and logical order is for any teacher in global analysis an interesting, important and fun creating task.

Author : Andrew McInerney
Publisher : Springer Science & Business Media
Page : 410 pages
File Size : 47,9 Mb
Release : 2013-07-09
Category : Mathematics
ISBN : 9781461477327

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First Steps in Differential Geometry by Andrew McInerney Pdf

Differential geometry arguably offers the smoothest transition from the standard university mathematics sequence of the first four semesters in calculus, linear algebra, and differential equations to the higher levels of abstraction and proof encountered at the upper division by mathematics majors. Today it is possible to describe differential geometry as "the study of structures on the tangent space," and this text develops this point of view. This book, unlike other introductory texts in differential geometry, develops the architecture necessary to introduce symplectic and contact geometry alongside its Riemannian cousin. The main goal of this book is to bring the undergraduate student who already has a solid foundation in the standard mathematics curriculum into contact with the beauty of higher mathematics. In particular, the presentation here emphasizes the consequences of a definition and the careful use of examples and constructions in order to explore those consequences.

Author : Robert Everist Greene,Shing-Tung Yau
Publisher : American Mathematical Soc.
Page : 560 pages
File Size : 48,6 Mb
Release : 1993
Category : Mathematics
ISBN : 9780821814949

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Differential Geometry: Partial Differential Equations on Manifolds by Robert Everist Greene,Shing-Tung Yau Pdf

The first of three parts comprising Volume 54, the proceedings of the Summer Research Institute on Differential Geometry, held at the University of California, Los Angeles, July 1990 (ISBN for the set is 0-8218-1493-1). Part 1 begins with a problem list by S.T. Yau, successor to his 1980 list ( Sem

Author : Loring W. Tu
Publisher : Springer
Page : 347 pages
File Size : 50,7 Mb
Release : 2017-06-01
Category : Mathematics
ISBN : 9783319550848

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Differential Geometry by Loring W. Tu Pdf

This text presents a graduate-level introduction to differential geometry for mathematics and physics students. The exposition follows the historical development of the concepts of connection and curvature with the goal of explaining the Chern–Weil theory of characteristic classes on a principal bundle. Along the way we encounter some of the high points in the history of differential geometry, for example, Gauss' Theorema Egregium and the Gauss–Bonnet theorem. Exercises throughout the book test the reader’s understanding of the material and sometimes illustrate extensions of the theory. Initially, the prerequisites for the reader include a passing familiarity with manifolds. After the first chapter, it becomes necessary to understand and manipulate differential forms. A knowledge of de Rham cohomology is required for the last third of the text. Prerequisite material is contained in author's text An Introduction to Manifolds, and can be learned in one semester. For the benefit of the reader and to establish common notations, Appendix A recalls the basics of manifold theory. Additionally, in an attempt to make the exposition more self-contained, sections on algebraic constructions such as the tensor product and the exterior power are included. Differential geometry, as its name implies, is the study of geometry using differential calculus. It dates back to Newton and Leibniz in the seventeenth century, but it was not until the nineteenth century, with the work of Gauss on surfaces and Riemann on the curvature tensor, that differential geometry flourished and its modern foundation was laid. Over the past one hundred years, differential geometry has proven indispensable to an understanding of the physical world, in Einstein's general theory of relativity, in the theory of gravitation, in gauge theory, and now in string theory. Differential geometry is also useful in topology, several complex variables, algebraic geometry, complex manifolds, and dynamical systems, among other fields. The field has even found applications to group theory as in Gromov's work and to probability theory as in Diaconis's work. It is not too far-fetched to argue that differential geometry should be in every mathematician's arsenal.

Author : A.N. Pressley
Publisher : Springer Science & Business Media
Page : 336 pages
File Size : 49,6 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9781447136965

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Elementary Differential Geometry by A.N. Pressley Pdf

Pressley assumes the reader knows the main results of multivariate calculus and concentrates on the theory of the study of surfaces. Used for courses on surface geometry, it includes intersting and in-depth examples and goes into the subject in great detail and vigour. The book will cover three-dimensional Euclidean space only, and takes the whole book to cover the material and treat it as a subject in its own right.

Author : Stefan Haesen,Leopold Verstraelen
Publisher : Springer
Page : 284 pages
File Size : 44,7 Mb
Release : 2016-12-21
Category : Mathematics
ISBN : 9789462392403

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Topics in Modern Differential Geometry by Stefan Haesen,Leopold Verstraelen Pdf

A variety of introductory articles is provided on a wide range of topics, including variational problems on curves and surfaces with anisotropic curvature. Experts in the fields of Riemannian, Lorentzian and contact geometry present state-of-the-art reviews of their topics. The contributions are written on a graduate level and contain extended bibliographies. The ten chapters are the result of various doctoral courses which were held in 2009 and 2010 at universities in Leuven, Serbia, Romania and Spain.

Author : Thierry Aubin
Publisher : Springer Science & Business Media
Page : 414 pages
File Size : 50,8 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9783662130063

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Some Nonlinear Problems in Riemannian Geometry by Thierry Aubin Pdf

This book deals with such important subjects as variational methods, the continuity method, parabolic equations on fiber bundles, ideas concerning points of concentration, blowing-up technique, geometric and topological methods. It explores important geometric problems that are of interest to many mathematicians and scientists but have only recently been partially solved.