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Fundamentals of Differential Geometry

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 417/5 ( reviews)

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Book Synopsis Fundamentals of Differential Geometry by : Serge Lang

Download or read book Fundamentals of Differential Geometry written by Serge Lang. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: 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

Foundations of Differential Geometry, Volume 2

1996-02-22 Mathematics
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Release : 1996-02-22
Genre : Mathematics
Kind : eBook
Book Rating : 328/5 ( reviews)

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Book Synopsis Foundations of Differential Geometry, Volume 2 by : Shoshichi Kobayashi

Download or read book Foundations of Differential Geometry, Volume 2 written by Shoshichi Kobayashi. This book was released on 1996-02-22. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Foundations of Arithmetic Differential Geometry

2017-06-09 Mathematics
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Release : 2017-06-09
Genre : Mathematics
Kind : eBook
Book Rating : 23X/5 ( reviews)

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Book Synopsis Foundations of Arithmetic Differential Geometry by : Alexandru Buium

Download or read book Foundations of Arithmetic Differential Geometry written by Alexandru Buium. This book was released on 2017-06-09. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to introduce and develop an arithmetic analogue of classical differential geometry. In this new geometry the ring of integers plays the role of a ring of functions on an infinite dimensional manifold. The role of coordinate functions on this manifold is played by the prime numbers. The role of partial derivatives of functions with respect to the coordinates is played by the Fermat quotients of integers with respect to the primes. The role of metrics is played by symmetric matrices with integer coefficients. The role of connections (respectively curvature) attached to metrics is played by certain adelic (respectively global) objects attached to the corresponding matrices. One of the main conclusions of the theory is that the spectrum of the integers is “intrinsically curved”; the study of this curvature is then the main task of the theory. The book follows, and builds upon, a series of recent research papers. A significant part of the material has never been published before.

Foundations of Differential Geometry, Volume 2

1963 Mathematics
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Release : 1963
Genre : Mathematics
Kind : eBook
Book Rating : /5 ( reviews)

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Book Synopsis Foundations of Differential Geometry, Volume 2 by : Shoshichi Kobayashi

Download or read book Foundations of Differential Geometry, Volume 2 written by Shoshichi Kobayashi. This book was released on 1963. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Foundations of Differentiable Manifolds and Lie Groups

2013-11-11 Mathematics
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Release : 2013-11-11
Genre : Mathematics
Kind : eBook
Book Rating : 997/5 ( reviews)

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Book Synopsis Foundations of Differentiable Manifolds and Lie Groups by : Frank W. Warner

Download or read book Foundations of Differentiable Manifolds and Lie Groups written by Frank W. Warner. This book was released on 2013-11-11. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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