Differential Geometry

Author: Heinrich W. Guggenheimer

Publisher: Courier Corporation

ISBN: 0486157202

Category: Mathematics

Page: 400

View: 8269

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 Geometry

Author: Erwin Kreyszig

Publisher: Courier Corporation

ISBN: 0486318621

Category: Mathematics

Page: 384

View: 8951

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: Wolfgang Kühnel

Publisher: American Mathematical Soc.

ISBN: 1470423200

Category: Curves

Page: 403

View: 1244

This carefully written book is an introduction to the beautiful ideas and results of differential geometry. The first half covers the geometry of curves and surfaces, which provide much of the motivation and intuition for the general theory. The second part studies the geometry of general manifolds, with particular emphasis on connections and curvature. The text is illustrated with many figures and examples. The prerequisites are undergraduate analysis and linear algebra. This new edition provides many advancements, including more figures and exercises, and--as a new feature--a good number of solutions to selected exercises.

Manifolds and Differential Geometry

Author: Jeffrey Marc Lee

Publisher: American Mathematical Soc.

ISBN: 0821848151

Category: Mathematics

Page: 671

View: 3757

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.

Differential Geometry: The Interface between Pure and Applied Mathematics

The Interface Between Pure and Applied Mathematics : Proceedings of a Conference Held April 23-25, 1986 with Support from the National Science Foundation

Author: Mladen Luksic,Clyde Martin

Publisher: American Mathematical Soc.

ISBN: 082185075X

Category: Mathematics

Page: 273

View: 2171

Normally, mathematical research has been divided into 'pure' and 'applied', and only within the past decade has this distinction become blurred. However, differential geometry is one area of mathematics that has not made this distinction and has consistently played a vital role in both general areas. The papers in this volume represent the proceedings of a conference entitled 'Differential Geometry: The Interface Between Pure and Applied Mathematics', which was held in San Antonio, Texas, in April 1986. The purpose of the conference was to explore recent exciting applications and challenging classical problems in differential geometry. The papers represent a tremendous range of applications and techniques in such diverse areas as ordinary differential equations, Lie groups, algebra, numerical analysis and control theory.

Differential Geometry

Author: J. J. Stoker

Publisher: John Wiley & Sons

ISBN: 1118165470

Category: Mathematics

Page: 432

View: 3374

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.

An Introduction to Differential Geometry

Author: T. J. Willmore

Publisher: Courier Corporation

ISBN: 0486282104

Category: Mathematics

Page: 336

View: 9363

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.

A Course in Differential Geometry

Author: Thierry Aubin

Publisher: American Mathematical Soc.

ISBN: 9780821872147

Category: Mathematics

Page: 184

View: 3256

This textbook for second-year graduate students is an introduction to differential geometry with principal emphasis on Riemannian geometry. 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.

Differential Geometry

Cartan's Generalization of Klein's Erlangen Program

Author: R.W. Sharpe

Publisher: Springer Science & Business Media

ISBN: 9780387947327

Category: Mathematics

Page: 421

View: 4764

Cartan geometries were the first examples of connections on a principal bundle. They seem to be almost unknown these days, in spite of the great beauty and conceptual power they confer on geometry. The aim of the present book is to fill the gap in the literature on differential geometry by the missing notion of Cartan connections. Although the author had in mind a book accessible to graduate students, potential readers would also include working differential geometers who would like to know more about what Cartan did, which was to give a notion of "espaces giniralisis" (= Cartan geometries) generalizing homogeneous spaces (= Klein geometries) in the same way that Riemannian geometry generalizes Euclidean geometry. In addition, physicists will be interested to see the fully satisfying way in which their gauge theory can be truly regarded as geometry.

Fundamentals of Differential Geometry

Author: Serge Lang

Publisher: Springer Science & Business Media

ISBN: 1461205417

Category: Mathematics

Page: 540

View: 9067

This book provides an introduction to the basic concepts in differential topology, differential geometry, and differential equations, and some of the main basic theorems in all three areas. This new edition includes new chapters, sections, examples, and exercises. From the reviews: "There are many books on the fundamentals of differential geometry, but this one is quite exceptional; this is not surprising for those who know Serge Lang's books." --EMS NEWSLETTER

Differential Geometry

Connections, Curvature, and Characteristic Classes

Author: Loring W. Tu

Publisher: Springer

ISBN: 3319550845

Category: Mathematics

Page: 347

View: 8239

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.

Differential Geometry

Author: Courant Institute of Mathematical Sciences

Publisher: Krishna Prakashan Media

ISBN: N.A

Category:

Page: N.A

View: 2467

DIFFERENTIAL GEOMETRY OF MANIFOLDS

Author: QUDDUS KHAN

Publisher: PHI Learning Pvt. Ltd.

ISBN: 8120346505

Category: Mathematics

Page: 256

View: 5936

Curves and surfaces are objects that everyone can see, and many of the questions that can be asked about them are natural and easily understood. Differential geometry is concerned with the precise mathematical formulation of some of these questions, while trying to answer them using calculus techniques. The geometry of differentiable manifolds with structures is one of the most important branches of modern differential geometry. This well-written book discusses the theory of differential and Riemannian manifolds to help students understand the basic structures and consequent developments. While introducing concepts such as bundles, exterior algebra and calculus, Lie group and its algebra and calculus, Riemannian geometry, submanifolds and hypersurfaces, almost complex manifolds, etc., enough care has been taken to provide necessary details which enable the reader to grasp them easily. The material of this book has been successfully tried in classroom teaching. The book is designed for the postgraduate students of Mathematics. It will also be useful to the researchers working in the field of differential geometry and its applications to general theory of relativity and cosmology, and other applied areas. KEY FEATURES  Provides basic concepts in an easy-to-understand style.  Presents the subject in a natural way.  Follows a coordinate-free approach.  Includes a large number of solved examples and illuminating illustrations.  Gives notes and remarks at appropriate places.

Differential Geometry

Author: William C. Graustein

Publisher: Courier Corporation

ISBN: 0486153231

Category: Mathematics

Page: 240

View: 4956

This first course in differential geometry presents the fundamentals of the metric differential geometry of curves and surfaces in a Euclidean space of 3 dimensions, using vector notation and technique. Nearly 200 problems.1935 edition.

Differential Geometry

Proceedings of the Symposium in Pure Mathematics of the American Mathematical Society, Held at Stanford University, Stanford, California, July 30-August 17, 1973

Author: Shiing-Shen Chern,Robert Osserman,American Mathematical Society

Publisher: American Mathematical Soc.

ISBN: 082180247X

Category: Mathematics

Page: 451

View: 3044

Contains sections on Riemannian geometry, Submanifolds, Foliations, Algebraic and piecewise linear topology, Miscellaneous

Differential Geometry of Curves and Surfaces

Author: Kristopher Tapp

Publisher: Springer

ISBN: 3319397990

Category: Mathematics

Page: 366

View: 8558

This is a textbook on differential geometry well-suited to a variety of courses on this topic. For readers seeking an elementary text, the prerequisites are minimal and include plenty of examples and intermediate steps within proofs, while providing an invitation to more excursive applications and advanced topics. For readers bound for graduate school in math or physics, this is a clear, concise, rigorous development of the topic including the deep global theorems. For the benefit of all readers, the author employs various techniques to render the difficult abstract ideas herein more understandable and engaging. Over 300 color illustrations bring the mathematics to life, instantly clarifying concepts in ways that grayscale could not. Green-boxed definitions and purple-boxed theorems help to visually organize the mathematical content. Color is even used within the text to highlight logical relationships. Applications abound! The study of conformal and equiareal functions is grounded in its application to cartography. Evolutes, involutes and cycloids are introduced through Christiaan Huygens' fascinating story: in attempting to solve the famous longitude problem with a mathematically-improved pendulum clock, he invented mathematics that would later be applied to optics and gears. Clairaut’s Theorem is presented as a conservation law for angular momentum. Green’s Theorem makes possible a drafting tool called a planimeter. Foucault’s Pendulum helps one visualize a parallel vector field along a latitude of the earth. Even better, a south-pointing chariot helps one visualize a parallel vector field along any curve in any surface. In truth, the most profound application of differential geometry is to modern physics, which is beyond the scope of this book. The GPS in any car wouldn’t work without general relativity, formalized through the language of differential geometry. Throughout this book, applications, metaphors and visualizations are tools that motivate and clarify the rigorous mathematical content, but never replace it.

Differential Geometry: Manifolds, Curves, and Surfaces

Manifolds, Curves, and Surfaces

Author: Marcel Berger,Bernard Gostiaux

Publisher: Springer Science & Business Media

ISBN: 146121033X

Category: Mathematics

Page: 476

View: 2572

This book consists of two parts, different in form but similar in spirit. The first, which comprises chapters 0 through 9, is a revised and somewhat enlarged version of the 1972 book Geometrie Differentielle. The second part, chapters 10 and 11, is an attempt to remedy the notorious absence in the original book of any treatment of surfaces in three-space, an omission all the more unforgivable in that surfaces are some of the most common geometrical objects, not only in mathematics but in many branches of physics. Geometrie Differentielle was based on a course I taught in Paris in 1969- 70 and again in 1970-71. In designing this course I was decisively influ enced by a conversation with Serge Lang, and I let myself be guided by three general ideas. First, to avoid making the statement and proof of Stokes' formula the climax of the course and running out of time before any of its applications could be discussed. Second, to illustrate each new notion with non-trivial examples, as soon as possible after its introduc tion. And finally, to familiarize geometry-oriented students with analysis and analysis-oriented students with geometry, at least in what concerns manifolds.

Handbook of Differential Geometry

Author: Franki J.E. Dillen,Leopold C.A. Verstraelen

Publisher: Elsevier

ISBN: 9780080461205

Category: Mathematics

Page: 574

View: 7866

In the series of volumes which together will constitute the "Handbook of Differential Geometry" we try to give a rather complete survey of the field of differential geometry. The different chapters will both deal with the basic material of differential geometry and with research results (old and recent). All chapters are written by experts in the area and contain a large bibliography. In this second volume a wide range of areas in the very broad field of differential geometry is discussed, as there are Riemannian geometry, Lorentzian geometry, Finsler geometry, symplectic geometry, contact geometry, complex geometry, Lagrange geometry and the geometry of foliations. Although this does not cover the whole of differential geometry, the reader will be provided with an overview of some its most important areas. . Written by experts and covering recent research . Extensive bibliography . Dealing with a diverse range of areas . Starting from the basics

Topics in Modern Differential Geometry

Author: Stefan Haesen,Leopold Verstraelen

Publisher: Springer

ISBN: 9462392404

Category: Mathematics

Page: 284

View: 6766

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.

Topics in Mathematical Analysis and Differential Geometry

Author: Nicolas K. Laos

Publisher: World Scientific

ISBN: 9789810231804

Category: Mathematics

Page: 559

View: 3181

This book studies the interplay between mathematical analysis and differential geometry as well as the foundations of these two fields. The development of a unified approach to topological vector spaces, differential geometry and algebraic and differential topology of function manifolds led to the broad expansion of global analysis. This book serves as a self-contained reference on both the prerequisites for further study and the recent research results which have played a decisive role in the advancement of global analysis.