# fundamentals of differential geometry graduate texts in mathematics

**Download Book Fundamentals Of Differential Geometry Graduate Texts In Mathematics in PDF format. You can Read Online Fundamentals Of Differential Geometry Graduate Texts In Mathematics here in PDF, EPUB, Mobi or Docx formats.**

## Fundamentals Of Differential Geometry

**Author :**Serge Lang

**ISBN :**9781461205418

**Genre :**Mathematics

**File Size :**64. 54 MB

**Format :**PDF, ePub, Mobi

**Download :**873

**Read :**189

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 And Riemannian Manifolds

**Author :**Serge Lang

**ISBN :**0387943382

**Genre :**Mathematics

**File Size :**27. 33 MB

**Format :**PDF, Kindle

**Download :**745

**Read :**1182

This book covers basic concepts in differential topology, differential geometry and differential equations. The latest, expanded edition offers three new chapters on Riemannian and pseudo-Riemannian geometry, and revised sections on sprays and Stokes' theorem.

## Foundations Of Differentiable Manifolds And Lie Groups

**Author :**Frank W. Warner

**ISBN :**9781475717990

**Genre :**Mathematics

**File Size :**88. 17 MB

**Format :**PDF, ePub, Mobi

**Download :**671

**Read :**278

Foundations of Differentiable Manifolds and Lie Groups gives a clear, detailed, and careful development of the basic facts on manifold theory and Lie Groups. Coverage includes differentiable manifolds, tensors and differentiable forms, Lie groups and homogenous spaces, and integration on manifolds. The book also provides a proof of the de Rham theorem via sheaf cohomology theory and develops the local theory of elliptic operators culminating in a proof of the Hodge theorem.

## Metric Structures In Differential Geometry

**Author :**Gerard Walschap

**ISBN :**9780387218267

**Genre :**Mathematics

**File Size :**35. 85 MB

**Format :**PDF, Docs

**Download :**720

**Read :**630

This book offers an introduction to the theory of differentiable manifolds and fiber bundles. It examines bundles from the point of view of metric differential geometry: Euclidean bundles, Riemannian connections, curvature, and Chern-Weil theory are discussed, including the Pontrjagin, Euler, and Chern characteristic classes of a vector bundle. These concepts are illustrated in detail for bundles over spheres.

## A Course In Differential Geometry

**Author :**W. Klingenberg

**ISBN :**9781461299233

**Genre :**Mathematics

**File Size :**90. 91 MB

**Format :**PDF, ePub

**Download :**120

**Read :**849

This English edition could serve as a text for a first year graduate course on differential geometry, as did for a long time the Chicago Notes of Chern mentioned in the Preface to the German Edition. Suitable references for ordin ary differential equations are Hurewicz, W. Lectures on ordinary differential equations. MIT Press, Cambridge, Mass., 1958, and for the topology of surfaces: Massey, Algebraic Topology, Springer-Verlag, New York, 1977. Upon David Hoffman fell the difficult task of transforming the tightly constructed German text into one which would mesh well with the more relaxed format of the Graduate Texts in Mathematics series. There are some e1aborations and several new figures have been added. I trust that the merits of the German edition have survived whereas at the same time the efforts of David helped to elucidate the general conception of the Course where we tried to put Geometry before Formalism without giving up mathematical rigour. 1 wish to thank David for his work and his enthusiasm during the whole period of our collaboration. At the same time I would like to commend the editors of Springer-Verlag for their patience and good advice. Bonn Wilhelm Klingenberg June,1977 vii From the Preface to the German Edition This book has its origins in a one-semester course in differential geometry which 1 have given many times at Gottingen, Mainz, and Bonn.

## Differential Geometry

**Author :**Loring W. Tu

**ISBN :**9783319550848

**Genre :**Mathematics

**File Size :**87. 79 MB

**Format :**PDF

**Download :**718

**Read :**1170

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 :**Clifford Henry Taubes

**ISBN :**9780191621222

**Genre :**Mathematics

**File Size :**58. 14 MB

**Format :**PDF, ePub, Mobi

**Download :**617

**Read :**1193

Bundles, connections, metrics and curvature are the 'lingua franca' of modern differential geometry and theoretical physics. This book will supply a graduate student in mathematics or theoretical physics with the fundamentals of these objects. Many of the tools used in differential topology are introduced and the basic results about differentiable manifolds, smooth maps, differential forms, vector fields, Lie groups, and Grassmanians are all presented here. Other material covered includes the basic theorems about geodesics and Jacobi fields, the classification theorem for flat connections, the definition of characteristic classes, and also an introduction to complex and Kähler geometry. Differential Geometry uses many of the classical examples from, and applications of, the subjects it covers, in particular those where closed form expressions are available, to bring abstract ideas to life. Helpfully, proofs are offered for almost all assertions throughout. All of the introductory material is presented in full and this is the only such source with the classical examples presented in detail.

## Differential Geometry

**Author :**R.W. Sharpe

**ISBN :**0387947329

**Genre :**Mathematics

**File Size :**88. 32 MB

**Format :**PDF, ePub

**Download :**104

**Read :**208

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.

## Riemannian Manifolds

**Author :**John M. Lee

**ISBN :**9780387982717

**Genre :**Mathematics

**File Size :**29. 92 MB

**Format :**PDF, ePub, Mobi

**Download :**762

**Read :**300

This unique volume will appeal especially to students by presenting a selective introduction to the main ideas of the subject in an easily accessible way. The material is ideal for a single course, but broad enough to provide students with a firm foundation from which to pursue research or develop applications in Riemannian geometry and other fields that use its tools.

## Topology And Geometry

**Author :**Glen E. Bredon

**ISBN :**9781475768480

**Genre :**Mathematics

**File Size :**52. 40 MB

**Format :**PDF, ePub, Mobi

**Download :**389

**Read :**1054

This book offers an introductory course in algebraic topology. Starting with general topology, it discusses differentiable manifolds, cohomology, products and duality, the fundamental group, homology theory, and homotopy theory. From the reviews: "An interesting and original graduate text in topology and geometry...a good lecturer can use this text to create a fine course....A beginning graduate student can use this text to learn a great deal of mathematics."—-MATHEMATICAL REVIEWS