[PDF] An Introduction To Riemannian Geometry And The Tensor Calculus eBook

Author : C. E. Weatherburn
Publisher : Cambridge University Press
Page : 191 pages
File Size : 23,99 MB
Release : 1938-01-02
Category : Mathematics
ISBN : 9780521067522

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The purpose of this book is to bridge the gap between differential geometry of Euclidean space of three dimensions and the more advanced work on differential geometry of generalised space. The subject is treated with the aid of the Tensor Calculus, which is associated with the names of Ricci and Levi-Civita; and the book provides an introduction both to this calculus and to Riemannian geometry. The geometry of subspaces has been considerably simplified by use of the generalized covariant differentiation introduced by Mayer in 1930, and successfully applied by other mathematicians.

Author : Leonor Godinho
Publisher : Springer
Page : 476 pages
File Size : 47,18 MB
Release : 2014-07-26
Category : Mathematics
ISBN : 3319086669

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Unlike many other texts on differential geometry, this textbook also offers interesting applications to geometric mechanics and general relativity. The first part is a concise and self-contained introduction to the basics of manifolds, differential forms, metrics and curvature. The second part studies applications to mechanics and relativity including the proofs of the Hawking and Penrose singularity theorems. It can be independently used for one-semester courses in either of these subjects. The main ideas are illustrated and further developed by numerous examples and over 300 exercises. Detailed solutions are provided for many of these exercises, making An Introduction to Riemannian Geometry ideal for self-study.

Author : T. J. Willmore
Publisher : Courier Corporation
Page : 338 pages
File Size : 35,60 MB
Release : 2013-05-13
Category : Mathematics
ISBN : 0486282104

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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.

Author : Luther Pfahler Eisenhart
Publisher : Princeton University Press
Page : 315 pages
File Size : 47,63 MB
Release : 2015-12-08
Category : Mathematics
ISBN : 1400877865

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Book 3 in the Princeton Mathematical Series. Originally published in 1950. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Author : Bernhard Riemann
Publisher : Birkhäuser
Page : 181 pages
File Size : 22,23 MB
Release : 2016-04-19
Category : Mathematics
ISBN : 3319260421

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This book presents William Clifford’s English translation of Bernhard Riemann’s classic text together with detailed mathematical, historical and philosophical commentary. The basic concepts and ideas, as well as their mathematical background, are provided, putting Riemann’s reasoning into the more general and systematic perspective achieved by later mathematicians and physicists (including Helmholtz, Ricci, Weyl, and Einstein) on the basis of his seminal ideas. Following a historical introduction that positions Riemann’s work in the context of his times, the history of the concept of space in philosophy, physics and mathematics is systematically presented. A subsequent chapter on the reception and influence of the text accompanies the reader from Riemann’s times to contemporary research. Not only mathematicians and historians of the mathematical sciences, but also readers from other disciplines or those with an interest in physics or philosophy will find this work both appealing and insightful.