differential geometric structures dover books on mathematics

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Differential Geometric Structures

Author : Walter A. Poor
ISBN : 9780486151915
Genre : Mathematics
File Size : 68. 73 MB
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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.

Differential Geometric Structures

Author : Walter A. Poor
ISBN : 9780486151915
Genre : Mathematics
File Size : 89. 19 MB
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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.

Differential Geometry

Author : Erwin Kreyszig
ISBN : 9780486318622
Genre : Mathematics
File Size : 20. 69 MB
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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
ISBN : 9780486157207
Genre : Mathematics
File Size : 88. 20 MB
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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.

Tensor Analysis On Manifolds

Author : Richard L. Bishop
ISBN : 9780486139234
Genre : Mathematics
File Size : 35. 4 MB
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DIVProceeds from general to special, including chapters on vector analysis on manifolds and integration theory. /div

Manifolds And Differential Geometry

Author : Jeffrey Marc Lee
ISBN : 9780821848159
Genre : Mathematics
File Size : 80. 35 MB
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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.

Modern Geometric Structures And Fields

Author : Сергей Петрович Новиков
ISBN : 9780821839294
Genre : Mathematics
File Size : 77. 40 MB
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The book presents the basics of Riemannian geometry in its modern form as geometry of differentiable manifolds and the most important structures on them. The authors' approach is that the source of all constructions in Riemannian geometry is a manifold that allows one to compute scalar products of tangent vectors. With this approach, the authors show that Riemannian geometry has a great influence to several fundamental areas of modern mathematics and its applications. In particular, Geometry is a bridge between pure mathematics and natural sciences, first of all physics. Fundamental laws of nature are formulated as relations between geometric fields describing various physical quantities. The study of global properties of geometric objects leads to the far-reaching development of topology, including topology and geometry of fiber bundles. Geometric theory of Hamiltonian systems, which describe many physical phenomena, led to the development of symplectic and Poisson geometry. Field theory and the multidimensional calculus of variations, presented in the book, unify mathematics with theoretical physics. Geometry of complex and algebraic manifolds unifies Riemannian geometry with modern complex analysis, as well as with algebra and number theory. Prerequisites for using the book include several basic undergraduate courses, such as advanced calculus, linear algebra, ordinary differential equations, and elements of topology.

Differential Manifolds

Author : Antoni A. Kosinski
ISBN : 9780486318158
Genre : Mathematics
File Size : 90. 31 MB
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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.

First Steps In Differential Geometry

Author : Andrew McInerney
ISBN : 9781461477327
Genre : Mathematics
File Size : 80. 84 MB
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Differential geometry arguably offers the smoothest transition from the standard university mathematics sequence of the first four semesters in calculus, linear algebra, and differential equations to the higher levels of abstraction and proof encountered at the upper division by mathematics majors. Today it is possible to describe differential geometry as "the study of structures on the tangent space," and this text develops this point of view. This book, unlike other introductory texts in differential geometry, develops the architecture necessary to introduce symplectic and contact geometry alongside its Riemannian cousin. The main goal of this book is to bring the undergraduate student who already has a solid foundation in the standard mathematics curriculum into contact with the beauty of higher mathematics. In particular, the presentation here emphasizes the consequences of a definition and the careful use of examples and constructions in order to explore those consequences.

Tensors Differential Forms And Variational Principles

Author : David Lovelock
ISBN : 9780486131986
Genre : Mathematics
File Size : 65. 66 MB
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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.

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