differential geometry

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Differential Geometry

Author : Heinrich W. Guggenheimer
ISBN : 9780486157207
Genre : Mathematics
File Size : 50. 50 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.

Differential Geometry

Author : J. J. Stoker
ISBN : 9781118165478
Genre : Mathematics
File Size : 65. 46 MB
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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.

Differential Geometry

Author : R.W. Sharpe
ISBN : 0387947329
Genre : Mathematics
File Size : 34. 41 MB
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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.

Differential Geometry

Author : Shiing-Shen Chern
ISBN : 9780821802472
Genre : Mathematics
File Size : 53. 79 MB
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Contains sections on Riemannian geometry, Submanifolds, Foliations, Algebraic and piecewise linear topology, Miscellaneous

An Introduction To Differential Geometry

Author : T. J. Willmore
ISBN : 9780486282107
Genre : Mathematics
File Size : 69. 11 MB
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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.

Differential Geometry

Author : William C. Graustein
ISBN : 9780486153230
Genre : Mathematics
File Size : 68. 73 MB
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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.

Manifolds And Differential Geometry

Author : Jeffrey Marc Lee
ISBN : 9780821848159
Genre : Mathematics
File Size : 65. 98 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.

Differential Geometry

Author : Courant Institute of Mathematical Sciences
ISBN :
Genre :
File Size : 38. 91 MB
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Differential Geometry

Author : Erwin Kreyszig
ISBN : 9780486318622
Genre : Mathematics
File Size : 40. 22 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.

Applicable Differential Geometry

Author : M. Crampin
ISBN : 0521231906
Genre : Mathematics
File Size : 32. 64 MB
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An introduction to geometrical topics used in applied mathematics and theoretical physics.

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