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Differential Geometry and Topology

Differential Geometry and Topology Author Keith Burns
ISBN-10 1584882530
Release 2005-05-27
Pages 400
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Accessible, concise, and self-contained, this book offers an outstanding introduction to three related subjects: differential geometry, differential topology, and dynamical systems. Topics of special interest addressed in the book include Brouwer's fixed point theorem, Morse Theory, and the geodesic flow. Smooth manifolds, Riemannian metrics, affine connections, the curvature tensor, differential forms, and integration on manifolds provide the foundation for many applications in dynamical systems and mechanics. The authors also discuss the Gauss-Bonnet theorem and its implications in non-Euclidean geometry models. The differential topology aspect of the book centers on classical, transversality theory, Sard's theorem, intersection theory, and fixed-point theorems. The construction of the de Rham cohomology builds further arguments for the strong connection between the differential structure and the topological structure. It also furnishes some of the tools necessary for a complete understanding of the Morse theory. These discussions are followed by an introduction to the theory of hyperbolic systems, with emphasis on the quintessential role of the geodesic flow. The integration of geometric theory, topological theory, and concrete applications to dynamical systems set this book apart. With clean, clear prose and effective examples, the authors' intuitive approach creates a treatment that is comprehensible to relative beginners, yet rigorous enough for those with more background and experience in the field.



Differential Geometry and Topology

Differential Geometry and Topology Author Keith Burns
ISBN-10 9781420057539
Release 2005-05-27
Pages 400
Download Link Click Here

Accessible, concise, and self-contained, this book offers an outstanding introduction to three related subjects: differential geometry, differential topology, and dynamical systems. Topics of special interest addressed in the book include Brouwer's fixed point theorem, Morse Theory, and the geodesic flow. Smooth manifolds, Riemannian metrics, affine connections, the curvature tensor, differential forms, and integration on manifolds provide the foundation for many applications in dynamical systems and mechanics. The authors also discuss the Gauss-Bonnet theorem and its implications in non-Euclidean geometry models. The differential topology aspect of the book centers on classical, transversality theory, Sard's theorem, intersection theory, and fixed-point theorems. The construction of the de Rham cohomology builds further arguments for the strong connection between the differential structure and the topological structure. It also furnishes some of the tools necessary for a complete understanding of the Morse theory. These discussions are followed by an introduction to the theory of hyperbolic systems, with emphasis on the quintessential role of the geodesic flow. The integration of geometric theory, topological theory, and concrete applications to dynamical systems set this book apart. With clean, clear prose and effective examples, the authors' intuitive approach creates a treatment that is comprehensible to relative beginners, yet rigorous enough for those with more background and experience in the field.



Basic Elements of Differential Geometry and Topology

Basic Elements of Differential Geometry and Topology Author S.P. Novikov
ISBN-10 9789401578950
Release 2013-03-14
Pages 490
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Basic Elements of Differential Geometry and Topology has been writing in one form or another for most of life. You can find so many inspiration from Basic Elements of Differential Geometry and Topology also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Basic Elements of Differential Geometry and Topology book for free.



A First Course in Geometric Topology and Differential Geometry

A First Course in Geometric Topology and Differential Geometry Author Ethan D. Bloch
ISBN-10 9780817681227
Release 2011-06-27
Pages 421
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A First Course in Geometric Topology and Differential Geometry has been writing in one form or another for most of life. You can find so many inspiration from A First Course in Geometric Topology and Differential Geometry also informative, and entertaining. Click DOWNLOAD or Read Online button to get full A First Course in Geometric Topology and Differential Geometry book for free.



Algebraic Topology Via Differential Geometry

Algebraic Topology Via Differential Geometry Author M. Karoubi
ISBN-10 0521317142
Release 1987-01
Pages 363
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In this volume the authors seek to illustrate how methods of differential geometry find application in the study of the topology of differential manifolds. Prerequisites are few since the authors take pains to set out the theory of differential forms and the algebra required. The reader is introduced to De Rham cohomology, and explicit and detailed calculations are present as examples. Topics covered include Mayer-Vietoris exact sequences, relative cohomology, Pioncare duality and Lefschetz's theorem. This book will be suitable for graduate students taking courses in algebraic topology and in differential topology. Mathematicians studying relativity and mathematical physics will find this an invaluable introduction to the techniques of differential geometry.



A short course in differential geometry and topology

A short course in differential geometry and topology Author A. T. Fomenko
ISBN-10 1904868320
Release 2009
Pages 273
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"This volume is intended for graduate and research students in mathematics and physics. It covers general topology, nonlinear co-ordinate systems, theory of smooth manifolds, theory of curves and surfaces, transformation groups, tensor analysis and Riemannian geometry, theory of integration and homologies, fundamental groups and variational principles in Riemannian geometry. The text is presented in a form that is easily accessible to students and is supplemented by a large number of examples, problems, drawings and appendices."--Cambridge Scientific Publishers website, viewed 2 September 2009.



Differential Geometry and Topology

Differential Geometry and Topology Author A.T. Fomenko
ISBN-10 9780306109959
Release 1987-05-31
Pages 344
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Differential Geometry and Topology has been writing in one form or another for most of life. You can find so many inspiration from Differential Geometry and Topology also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Differential Geometry and Topology book for free.



Differential Geometry and Topology of Curves

Differential Geometry and Topology of Curves Author Yu Animov
ISBN-10 9781420022605
Release 2001-01-11
Pages 216
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Differential geometry is an actively developing area of modern mathematics. This volume presents a classical approach to the general topics of the geometry of curves, including the theory of curves in n-dimensional Euclidean space. The author investigates problems for special classes of curves and gives the working method used to obtain the conditions for closed polygonal curves. The proof of the Bakel-Werner theorem in conditions of boundedness for curves with periodic curvature and torsion is also presented. This volume also highlights the contributions made by great geometers. past and present, to differential geometry and the topology of curves.



An Introduction to Differential Geometry and Topology in Mathematical Physics

An Introduction to Differential Geometry and Topology in Mathematical Physics Author Wang Rong
ISBN-10 9789814495806
Release 1999-01-18
Pages 220
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This book gives an outline of the developments of differential geometry and topology in the twentieth century, especially those which will be closely related to new discoveries in theoretical physics. Contents:Differential Manifolds:Preliminary Knowledge and DefinitionsProperties and Operations of Tangent Vectors and Cotangent VectorsCurvature Tensors, Torsion Tensors, Covariant Differentials and Adjoint Exterior DifferentialsRiemannian GeometryComplex ManifoldGlobal Topological Properties:Homotopy Equivalence and Homotopy Groups of ManifoldsHomology and de Rham CohomologyFibre Bundles and Their Topological StructuresConnections and Curvatures on Fibre BundlesCharacteristic Classes of Fibre BundlesIndex Theorem and 4-Manifolds:Index Theorems for Manifolds Without BoundaryEssential Features of 4-Manifolds Readership: Mathematicians and physicists. Keywords:Homotopy Theory;Index Theorems;Riemannian Geometry;Complex Manifolds;Homology;De Rham Cohomology;Fibre Bundles;Characteristic Classes



A course of differential geometry and topology

A course of differential geometry and topology Author Aleksandr Sergeevich Mishchenko
ISBN-10 UOM:39076000924121
Release 1988
Pages 455
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A course of differential geometry and topology has been writing in one form or another for most of life. You can find so many inspiration from A course of differential geometry and topology also informative, and entertaining. Click DOWNLOAD or Read Online button to get full A course of differential geometry and topology book for free.



Modern Differential Geometry for Physicists

Modern Differential Geometry for Physicists Author Chris J. Isham
ISBN-10 8177643169
Release 2002-01-01
Pages 290
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Modern Differential Geometry for Physicists has been writing in one form or another for most of life. You can find so many inspiration from Modern Differential Geometry for Physicists also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Modern Differential Geometry for Physicists book for free.



Differential Geometry and Topology Discrete and Computational Geometry

Differential Geometry and Topology  Discrete and Computational Geometry Author Mohamed Boucetta
ISBN-10 9781586035075
Release 2005-01-01
Pages 373
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The aim of this volume is to give an introduction and overview to differential topology, differential geometry and computational geometry with an emphasis on some interconnections between these three domains of mathematics. The chapters give the background required to begin research in these fields or at their interfaces. They introduce new research domains and both old and new conjectures in these different subjects show some interaction between other sciences close to mathematics. Topics discussed are; the basis of differential topology and combinatorial topology, the link between differential geometry and topology, Riemanian geometry (Levi-Civita connextion, curvature tensor, geodesic, completeness and curvature tensor), characteristic classes (to associate every fibre bundle with isomorphic fiber bundles), the link between differential geometry and the geometry of non smooth objects, computational geometry and concrete applications such as structural geology and graphism.



Topology and Geometry for Physicists

Topology and Geometry for Physicists Author Charles Nash
ISBN-10 9780486318363
Release 2013-08-16
Pages 320
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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 Topology

Differential Topology Author Morris W. Hirsch
ISBN-10 9781468494495
Release 2012-12-06
Pages 222
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"A very valuable book. In little over 200 pages, it presents a well-organized and surprisingly comprehensive treatment of most of the basic material in differential topology, as far as is accessible without the methods of algebraic topology....There is an abundance of exercises, which supply many beautiful examples and much interesting additional information, and help the reader to become thoroughly familiar with the material of the main text." —MATHEMATICAL REVIEWS



Differential Geometry

Differential Geometry Author Erwin Kreyszig
ISBN-10 9780486318622
Release 2013-04-26
Pages 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.



Geometry and Topology of Submanifolds X

Geometry and Topology of Submanifolds X Author W H Chen
ISBN-10 9789814492034
Release 2000-11-07
Pages 360
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Contents:Progress in Affine Differential Geometry — Problem List and Continued Bibliography (T Binder & U Simon)On the Classification of Timelike Bonnet Surfaces (W H Chen & H Z Li)Affine Hyperspheres with Constant Affine Sectional Curvature (F Dillen et al.)Geometric Properties of the Curvature Operator (P Gilkey)On a Question of S S Chern Concerning Minimal Hypersurfaces of Spheres (I Hiric( & L Verstraelen)Parallel Pure Spinors on Pseudo-Riemannian Manifolds (I Kath)Twistorial Construction of Spacelike Surfaces in Lorentzian 4-Manifolds (F Leitner)Nirenberg's Problem in 90's (L Ma)A New Proof of the Homogeneity of Isoparametric Hypersurfaces with (g,m) = (6, 1) (R Miyaoka)Harmonic Maps and Negatively Curved Homogeneous Spaces (S Nishikawa)Biharmonic Morphisms Between Riemannian Manifolds (Y L Ou)Intrinsic Properties of Real Hypersurfaces in Complex Space Forms (P J Ryan)On the Nonexistence of Stable Minimal Submanifolds in Positively Pinched Riemannian Manifolds (Y B Shen & H Q Xu)Geodesic Mappings of the Ellipsoid (K Voss)η-Invariants and the Poincaré-Hopf Index Formula (W Zhang)and other papers Readership: Researchers in differential geometry and topology. Keywords:Conference;Proceedings;Berlin (Germany);Beijing (China);Geometry;Topology;Submanifolds X;Differential Geometry;Dedication



Manifolds and Differential Geometry

Manifolds and Differential Geometry Author Jeffrey Marc Lee
ISBN-10 9780821848159
Release 2009
Pages 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.