Differential Geometry

Author: Erwin Kreyszig

Publisher: Courier Corporation

ISBN: 0486318621

Category: Mathematics

Page: 384

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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.

Differential Geometry

Author: Heinrich W. Guggenheimer

Publisher: Courier Corporation

ISBN: 0486157202

Category: Mathematics

Page: 400

View: 5713

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This text contains an elementary introduction to continuous groups and differential invariants; an extensive treatment of groups of motions in euclidean, affine, and riemannian geometry; more. Includes exercises and 62 figures.

Differential Geometric Structures

Author: Walter A. Poor

Publisher: Courier Corporation

ISBN: 0486151913

Category: Mathematics

Page: 352

View: 7336

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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.

Tensor and Vector Analysis

With Applications to Differential Geometry

Author: C. E. Springer

Publisher: Courier Corporation

ISBN: 048632091X

Category: Mathematics

Page: 256

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Assuming only a knowledge of basic calculus, this text's elementary development of tensor theory focuses on concepts related to vector analysis. The book also forms an introduction to metric differential geometry. 1962 edition.

Curvature in Mathematics and Physics

Author: Shlomo Sternberg

Publisher: Courier Corporation

ISBN: 0486292711

Category: Mathematics

Page: 416

View: 9021

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Expert treatment introduces semi-Riemannian geometry and its principal physical application, Einstein's theory of general relativity, using the Cartan exterior calculus as a principal tool. Prerequisites include linear algebra and advanced calculus. 2012 edition.

Tensors, Differential Forms, and Variational Principles

Author: David Lovelock,Hanno Rund

Publisher: Courier Corporation

ISBN: 048613198X

Category: Mathematics

Page: 400

View: 2917

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Incisive, self-contained account of tensor analysis and the calculus of exterior differential forms, interaction between the concept of invariance and the calculus of variations. Emphasis is on analytical techniques. Includes problems.

Tensor Analysis on Manifolds

Author: Richard L. Bishop,Samuel I. Goldberg

Publisher: Courier Corporation

ISBN: 0486139239

Category: Mathematics

Page: 288

View: 909

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DIVProceeds from general to special, including chapters on vector analysis on manifolds and integration theory. /div

Lectures on Classical Differential Geometry

Author: Dirk Jan Struik

Publisher: Courier Corporation

ISBN: 9780486656090

Category: Mathematics

Page: 232

View: 4268

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Elementary, yet authoritative and scholarly, this book offers an excellent brief introduction to the classical theory of differential geometry. It is aimed at advanced undergraduate and graduate students who will find it not only highly readable but replete with illustrations carefully selected to help stimulate the student's visual understanding of geometry. The text features an abundance of problems, most of which are simple enough for class use, and often convey an interesting geometrical fact. A selection of more difficult problems has been included to challenge the ambitious student. Written by a noted mathematician and historian of mathematics, this volume presents the fundamental conceptions of the theory of curves and surfaces and applies them to a number of examples. Dr. Struik has enhanced the treatment with copious historical, biographical, and bibliographical references that place the theory in context and encourage the student to consult original sources and discover additional important ideas there. For this second edition, Professor Struik made some corrections and added an appendix with a sketch of the application of Cartan's method of Pfaffians to curve and surface theory. The result was to further increase the merit of this stimulating, thought-provoking text — ideal for classroom use, but also perfectly suited for self-study. In this attractive, inexpensive paperback edition, it belongs in the library of any mathematician or student of mathematics interested in differential geometry.

An Introduction to Differential Geometry

Author: T. J. Willmore

Publisher: Courier Corporation

ISBN: 0486282104

Category: Mathematics

Page: 336

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This text employs vector methods to explore the classical theory of curves and surfaces. Topics include basic theory of tensor algebra, tensor calculus, calculus of differential forms, and elements of Riemannian geometry. 1959 edition.

Differential Geometry of Curves and Surfaces

Revised and Updated Second Edition

Author: Manfredo P. do Carmo

Publisher: Courier Dover Publications

ISBN: 0486806995

Category: Mathematics

Page: 512

View: 4027

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One of the most widely used texts in its field, this volume introduces the differential geometry of curves and surfaces in both local and global aspects. The presentation departs from the traditional approach with its more extensive use of elementary linear algebra and its emphasis on basic geometrical facts rather than machinery or random details. Many examples and exercises enhance the clear, well-written exposition, along with hints and answers to some of the problems. The treatment begins with a chapter on curves, followed by explorations of regular surfaces, the geometry of the Gauss map, the intrinsic geometry of surfaces, and global differential geometry. Suitable for advanced undergraduates and graduate students of mathematics, this text's prerequisites include an undergraduate course in linear algebra and some familiarity with the calculus of several variables. For this second edition, the author has corrected, revised, and updated the entire volume.

Topology and Geometry for Physicists

Author: Charles Nash,Siddhartha Sen

Publisher: Courier Corporation

ISBN: 0486318362

Category: Mathematics

Page: 320

View: 9746

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Differential geometry and topology are essential tools for many theoretical physicists, particularly in the study of condensed matter physics, gravity, and particle physics. Written by physicists for physics students, this text introduces geometrical and topological methods in theoretical physics and applied mathematics. It assumes no detailed background in topology or geometry, and it emphasizes physical motivations, enabling students to apply the techniques to their physics formulas and research. "Thoroughly recommended" by The Physics Bulletin, this volume's physics applications range from condensed matter physics and statistical mechanics to elementary particle theory. Its main mathematical topics include differential forms, homotopy, homology, cohomology, fiber bundles, connection and covariant derivatives, and Morse theory.

Differential Manifolds

Author: Antoni A. Kosinski

Publisher: Courier Corporation

ISBN: 048631815X

Category: Mathematics

Page: 288

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Introductory text for advanced undergraduates and graduate students presents systematic study of the topological structure of smooth manifolds, starting with elements of theory and concluding with method of surgery. 1993 edition.

Introduction to Differential Geometry and Riemannian Geometry

Author: Erwin Kreyszig

Publisher: University of Toronto Press

ISBN: 1487591055

Category: Education

Page: 382

View: 7171

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This book provides an introduction to the differential geometry of curves and surfaces in three-dimensional Euclidean space and to n-dimensional Riemannian geometry. Based on Kreyszig's earlier book Differential Geometry, it is presented in a simple and understandable manner with many examples illustrating the ideas, methods, and results. Among the topics covered are vector and tensor algebra, the theory of surfaces, the formulae of Weingarten and Gauss, geodesics, mappings of surfaces and their applications, and global problems. A thorough investigation of Reimannian manifolds is made, including the theory of hypersurfaces. Interesting problems are provided and complete solutions are given at the end of the book together with a list of the more important formulae. Elementary calculus is the sole prerequisite for the understanding of this detailed and complete study in mathematics.

Introduction to Differentiable Manifolds

Author: Louis Auslander,Robert E. MacKenzie

Publisher: Courier Corporation

ISBN: 048615808X

Category: Mathematics

Page: 224

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This text presents basic concepts in the modern approach to differential geometry. Topics include Euclidean spaces, submanifolds, and abstract manifolds; fundamental concepts of Lie theory; fiber bundles; and multilinear algebra. 1963 edition.

Lectures on Differential Geometry

Author: S S Chern,W H Chen,K S Lam

Publisher: World Scientific Publishing Company

ISBN: 9813102985

Category: Mathematics

Page: 368

View: 4781

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This book is a translation of an authoritative introductory text based on a lecture series delivered by the renowned differential geometer, Professor S S Chern in Beijing University in 1980. The original Chinese text, authored by Professor Chern and Professor Wei-Huan Chen, was a unique contribution to the mathematics literature, combining simplicity and economy of approach with depth of contents. The present translation is aimed at a wide audience, including (but not limited to) advanced undergraduate and graduate students in mathematics, as well as physicists interested in the diverse applications of differential geometry to physics. In addition to a thorough treatment of the fundamentals of manifold theory, exterior algebra, the exterior calculus, connections on fiber bundles, Riemannian geometry, Lie groups and moving frames, and complex manifolds (with a succinct introduction to the theory of Chern classes), and an appendix on the relationship between differential geometry and theoretical physics, this book includes a new chapter on Finsler geometry and a new appendix on the history and recent developments of differential geometry, the latter prepared specially for this edition by Professor Chern to bring the text into perspectives.

Elementary Differential Geometry

Author: A.N. Pressley

Publisher: Springer Science & Business Media

ISBN: 1848828918

Category: Mathematics

Page: 474

View: 7391

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Elementary Differential Geometry presents the main results in the differential geometry of curves and surfaces suitable for a first course on the subject. Prerequisites are kept to an absolute minimum – nothing beyond first courses in linear algebra and multivariable calculus – and the most direct and straightforward approach is used throughout. New features of this revised and expanded second edition include: a chapter on non-Euclidean geometry, a subject that is of great importance in the history of mathematics and crucial in many modern developments. The main results can be reached easily and quickly by making use of the results and techniques developed earlier in the book. Coverage of topics such as: parallel transport and its applications; map colouring; holonomy and Gaussian curvature. Around 200 additional exercises, and a full solutions manual for instructors, available via www.springer.com ul>

Cohomology and Differential Forms

Author: Izu Vaisman

Publisher: Courier Dover Publications

ISBN: 0486804836

Category: Mathematics

Page: 304

View: 9903

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This monograph explores the cohomological theory of manifolds with various sheaves and its application to differential geometry. Based on lectures given by author Izu Vaisman at Romania's University of Iasi, the treatment is suitable for advanced undergraduates and graduate students of mathematics as well as mathematical researchers in differential geometry, global analysis, and topology. A self-contained development of cohomological theory constitutes the central part of the book. Topics include categories and functors, the Čech cohomology with coefficients in sheaves, the theory of fiber bundles, and differentiable, foliated, and complex analytic manifolds. The final chapter covers the theorems of de Rham and Dolbeault-Serre and examines the theorem of Allendoerfer and Eells, with applications of these theorems to characteristic classes and the general theory of harmonic forms.

Vector and Tensor Analysis with Applications

Author: A. I. Borisenko,I. E. Tarapov

Publisher: Courier Corporation

ISBN: 0486131904

Category: Mathematics

Page: 288

View: 5005

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Concise, readable text ranges from definition of vectors and discussion of algebraic operations on vectors to the concept of tensor and algebraic operations on tensors. Worked-out problems and solutions. 1968 edition.

Manifolds and Differential Geometry

Author: Jeffrey Marc Lee

Publisher: American Mathematical Soc.

ISBN: 0821848151

Category: Mathematics

Page: 671

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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 hyper-surfaces 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.