Fundamentals Of Differential Geometry

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Fundamentals of Differential Geometry

Serge Lang
Fundamentals of Differential Geometry Book PDF

Author : Serge Lang
Publisher : Springer Science & Business Media
Page : 553 pages
File Size : 54,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461205418

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Fundamentals of Differential Geometry by Serge Lang Pdf

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

Serge Lang
Differential and Riemannian Manifolds Book PDF

Author : Serge Lang
Publisher : Springer Science & Business Media
Page : 376 pages
File Size : 48,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461241829

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Differential and Riemannian Manifolds by Serge Lang Pdf

This is the third version of a book on differential manifolds. The first version appeared in 1962, and was written at the very beginning of a period of great expansion of the subject. At the time, I found no satisfactory book for the foundations of the subject, for multiple reasons. I expanded the book in 1971, and I expand it still further today. Specifically, I have added three chapters on Riemannian and pseudo Riemannian geometry, that is, covariant derivatives, curvature, and some applications up to the Hopf-Rinow and Hadamard-Cartan theorems, as well as some calculus of variations and applications to volume forms. I have rewritten the sections on sprays, and I have given more examples of the use of Stokes' theorem. I have also given many more references to the literature, all of this to broaden the perspective of the book, which I hope can be used among things for a general course leading into many directions. The present book still meets the old needs, but fulfills new ones. At the most basic level, the book gives an introduction to the basic concepts which are used in differential topology, differential geometry, and differential equations. In differential topology, one studies for instance homotopy classes of maps and the possibility of finding suitable differentiable maps in them (immersions, embeddings, isomorphisms, etc.).

Topics in Differential Geometry

Peter W. Michor
Topics in Differential Geometry Book PDF

Author : Peter W. Michor
Publisher : American Mathematical Soc.
Page : 510 pages
File Size : 48,7 Mb
Release : 2008
Category : Geometry, Differential
ISBN : 9780821820032

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Topics in Differential Geometry by Peter W. Michor Pdf

"This book treats the fundamentals of differential geometry: manifolds, flows, Lie groups and their actions, invariant theory, differential forms and de Rham cohomology, bundles and connections, Riemann manifolds, isometric actions, and symplectic and Poisson geometry. It gives the careful reader working knowledge in a wide range of topics of modern coordinate-free differential geometry in not too many pages. A prerequisite for using this book is a good knowledge of undergraduate analysis and linear algebra."--BOOK JACKET.

Foundations of Differential Geometry, Volume 2

Shoshichi Kobayashi,Katsumi Nomizu
Foundations of Differential Geometry Volume 2 Book PDF

Author : Shoshichi Kobayashi,Katsumi Nomizu
Publisher : University of Texas Press
Page : 492 pages
File Size : 49,8 Mb
Release : 1996-02-22
Category : Mathematics
ISBN : 0471157325

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Foundations of Differential Geometry, Volume 2 by Shoshichi Kobayashi,Katsumi Nomizu Pdf

This two-volume introduction to differential geometry, part of Wiley's popular Classics Library, lays the foundation for understanding an area of study that has become vital to contemporary mathematics. It is completely self-contained and will serve as a reference as well as a teaching guide. Volume 1 presents a systematic introduction to the field from a brief survey of differentiable manifolds, Lie groups and fibre bundles to the extension of local transformations and Riemannian connections. The second volume continues with the study of variational problems on geodesics through differential geometric aspects of characteristic classes. Both volumes familiarize readers with basic computational techniques.

Differential Geometry

Clifford Taubes
Differential Geometry Book PDF

Author : Clifford Taubes
Publisher : Oxford University Press on Demand
Page : 313 pages
File Size : 51,8 Mb
Release : 2011-10-13
Category : Mathematics
ISBN : 9780199605880

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Differential Geometry by Clifford Taubes Pdf

Bundles, connections, metrics and curvature are the lingua franca of modern differential geometry and theoretical physics. Supplying graduate students in mathematics or theoretical physics with the fundamentals of these objects, this book would suit a one-semester course on the subject of bundles and the associated geometry.

Foundations of Differentiable Manifolds and Lie Groups

Frank W. Warner
Foundations of Differentiable Manifolds and Lie Groups Book PDF

Author : Frank W. Warner
Publisher : Springer Science & Business Media
Page : 283 pages
File Size : 42,6 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9781475717990

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Foundations of Differentiable Manifolds and Lie Groups by Frank W. Warner Pdf

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.

Introduction to Differential Geometry

Joel W. Robbin,Dietmar A. Salamon
Introduction to Differential Geometry Book PDF

Author : Joel W. Robbin,Dietmar A. Salamon
Publisher : Springer Nature
Page : 426 pages
File Size : 55,8 Mb
Release : 2022-01-12
Category : Mathematics
ISBN : 9783662643402

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Introduction to Differential Geometry by Joel W. Robbin,Dietmar A. Salamon Pdf

This textbook is suitable for a one semester lecture course on differential geometry for students of mathematics or STEM disciplines with a working knowledge of analysis, linear algebra, complex analysis, and point set topology. The book treats the subject both from an extrinsic and an intrinsic view point. The first chapters give a historical overview of the field and contain an introduction to basic concepts such as manifolds and smooth maps, vector fields and flows, and Lie groups, leading up to the theorem of Frobenius. Subsequent chapters deal with the Levi-Civita connection, geodesics, the Riemann curvature tensor, a proof of the Cartan-Ambrose-Hicks theorem, as well as applications to flat spaces, symmetric spaces, and constant curvature manifolds. Also included are sections about manifolds with nonpositive sectional curvature, the Ricci tensor, the scalar curvature, and the Weyl tensor. An additional chapter goes beyond the scope of a one semester lecture course and deals with subjects such as conjugate points and the Morse index, the injectivity radius, the group of isometries and the Myers-Steenrod theorem, and Donaldson's differential geometric approach to Lie algebra theory.

Metric Structures in Differential Geometry

Gerard Walschap
Metric Structures in Differential Geometry Book PDF

Author : Gerard Walschap
Publisher : Springer Science & Business Media
Page : 235 pages
File Size : 45,8 Mb
Release : 2012-08-23
Category : Mathematics
ISBN : 9780387218267

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Metric Structures in Differential Geometry by Gerard Walschap Pdf

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.

An Introduction to Differential Geometry

T. J. Willmore
An Introduction to Differential Geometry Book PDF

Author : T. J. Willmore
Publisher : Courier Corporation
Page : 336 pages
File Size : 42,6 Mb
Release : 2013-05-13
Category : Mathematics
ISBN : 9780486282107

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An Introduction to Differential Geometry by T. J. Willmore Pdf

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.

Introduction to Geometry and Topology

Werner Ballmann
Introduction to Geometry and Topology Book PDF

Author : Werner Ballmann
Publisher : Birkhäuser
Page : 169 pages
File Size : 44,6 Mb
Release : 2018-07-18
Category : Mathematics
ISBN : 9783034809832

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Introduction to Geometry and Topology by Werner Ballmann Pdf

This book provides an introduction to topology, differential topology, and differential geometry. It is based on manuscripts refined through use in a variety of lecture courses. The first chapter covers elementary results and concepts from point-set topology. An exception is the Jordan Curve Theorem, which is proved for polygonal paths and is intended to give students a first glimpse into the nature of deeper topological problems. The second chapter of the book introduces manifolds and Lie groups, and examines a wide assortment of examples. Further discussion explores tangent bundles, vector bundles, differentials, vector fields, and Lie brackets of vector fields. This discussion is deepened and expanded in the third chapter, which introduces the de Rham cohomology and the oriented integral and gives proofs of the Brouwer Fixed-Point Theorem, the Jordan-Brouwer Separation Theorem, and Stokes's integral formula. The fourth and final chapter is devoted to the fundamentals of differential geometry and traces the development of ideas from curves to submanifolds of Euclidean spaces. Along the way, the book discusses connections and curvature--the central concepts of differential geometry. The discussion culminates with the Gauß equations and the version of Gauß's theorema egregium for submanifolds of arbitrary dimension and codimension. This book is primarily aimed at advanced undergraduates in mathematics and physics and is intended as the template for a one- or two-semester bachelor's course.

Differential Geometry and Statistics

M.K. Murray
Differential Geometry and Statistics Book PDF

Author : M.K. Murray
Publisher : Routledge
Page : 164 pages
File Size : 43,9 Mb
Release : 2017-10-19
Category : Mathematics
ISBN : 9781351455114

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Differential Geometry and Statistics by M.K. Murray Pdf

Several years ago our statistical friends and relations introduced us to the work of Amari and Barndorff-Nielsen on applications of differential geometry to statistics. This book has arisen because we believe that there is a deep relationship between statistics and differential geometry and moreoever that this relationship uses parts of differential geometry, particularly its 'higher-order' aspects not readily accessible to a statistical audience from the existing literature. It is, in part, a long reply to the frequent requests we have had for references on differential geometry! While we have not gone beyond the path-breaking work of Amari and Barndorff- Nielsen in the realm of applications, our book gives some new explanations of their ideas from a first principles point of view as far as geometry is concerned. In particular it seeks to explain why geometry should enter into parametric statistics, and how the theory of asymptotic expansions involves a form of higher-order differential geometry. The first chapter of the book explores exponential families as flat geometries. Indeed the whole notion of using log-likelihoods amounts to exploiting a particular form of flat space known as an affine geometry, in which straight lines and planes make sense, but lengths and angles are absent. We use these geometric ideas to introduce the notion of the second fundamental form of a family whose vanishing characterises precisely the exponential families.

Introduction to Differentiable Manifolds

Serge Lang
Introduction to Differentiable Manifolds Book PDF

Author : Serge Lang
Publisher : Springer Science & Business Media
Page : 250 pages
File Size : 46,8 Mb
Release : 2006-04-10
Category : Mathematics
ISBN : 9780387217727

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Introduction to Differentiable Manifolds by Serge Lang Pdf

Author is well-known and established book author (all Serge Lang books are now published by Springer); Presents a brief introduction to the subject; All manifolds are assumed finite dimensional in order not to frighten some readers; Complete proofs are given; Use of manifolds cuts across disciplines and includes physics, engineering and economics

Fundamentals of Advanced Mathematics V3

Henri Bourles
Fundamentals of Advanced Mathematics V3 Book PDF

Author : Henri Bourles
Publisher : Elsevier
Page : 424 pages
File Size : 49,5 Mb
Release : 2019-10-11
Category : Mathematics
ISBN : 9780081023860

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Fundamentals of Advanced Mathematics V3 by Henri Bourles Pdf

Fundamentals of Advanced Mathematics, Volume Three, begins with the study of differential and analytic infinite-dimensional manifolds, then progresses into fibered bundles, in particular, tangent and cotangent bundles. In addition, subjects covered include the tensor calculus on manifolds, differential and integral calculus on manifolds (general Stokes formula, integral curves and manifolds), an analysis on Lie groups, the Haar measure, the convolution of functions and distributions, and the harmonic analysis over a Lie group. Finally, the theory of connections is (linear connections, principal connections, and Cartan connections) covered, as is the calculus of variations in Lagrangian and Hamiltonian formulations. This volume is the prerequisite to the analytic and geometric study of nonlinear systems. Includes sections on differential and analytic manifolds, vector bundles, tensors, Lie derivatives, applications to algebraic topology, and more Presents an ideal prerequisite resource on the analytic and geometric study of nonlinear systems Provides theory as well as practical information

Elementary Differential Geometry

A.N. Pressley
Elementary Differential Geometry Book PDF

Author : A.N. Pressley
Publisher : Springer Science & Business Media
Page : 474 pages
File Size : 48,8 Mb
Release : 2010-03-10
Category : Mathematics
ISBN : 9781848828919

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Elementary Differential Geometry by A.N. Pressley Pdf

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

Elementary Differential Geometry

Barrett O'Neill
Elementary Differential Geometry Book PDF

Author : Barrett O'Neill
Publisher : Academic Press
Page : 422 pages
File Size : 46,6 Mb
Release : 2014-05-12
Category : Mathematics
ISBN : 9781483268118

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Elementary Differential Geometry by Barrett O'Neill Pdf

Elementary Differential Geometry focuses on the elementary account of the geometry of curves and surfaces. The book first offers information on calculus on Euclidean space and frame fields. Topics include structural equations, connection forms, frame fields, covariant derivatives, Frenet formulas, curves, mappings, tangent vectors, and differential forms. The publication then examines Euclidean geometry and calculus on a surface. Discussions focus on topological properties of surfaces, differential forms on a surface, integration of forms, differentiable functions and tangent vectors, congruence of curves, derivative map of an isometry, and Euclidean geometry. The manuscript takes a look at shape operators, geometry of surfaces in E, and Riemannian geometry. Concerns include geometric surfaces, covariant derivative, curvature and conjugate points, Gauss-Bonnet theorem, fundamental equations, global theorems, isometries and local isometries, orthogonal coordinates, and integration and orientation. The text is a valuable reference for students interested in elementary differential geometry.