Riemannian Geometry

Luther Pfahler Eisenhart

Published by Princeton University Press 1950

Riemannian Geometry

Luther Pfahler Eisenhart

Volume 51 in the series Princeton Landmarks in Mathematics and Physics

https://doi.org/10.1515/9781400884216

Overview
Contents

About this book

In his classic work of geometry, Euclid focused on the properties of flat surfaces. In the age of exploration, mapmakers such as Mercator had to concern themselves with the properties of spherical surfaces. The study of curved surfaces, or non-Euclidean geometry, flowered in the late nineteenth century, as mathematicians such as Riemann increasingly questioned Euclid's parallel postulate, and by relaxing this constraint derived a wealth of new results. These seemingly abstract properties found immediate application in physics upon Einstein's introduction of the general theory of relativity.

In this book, Eisenhart succinctly surveys the key concepts of Riemannian geometry, addressing mathematicians and theoretical physicists alike.

Reviews

Eisenhart's classic work on the application of tensor calculus to geometry was originally published in 1926 . . . It is still one of the best accounts of the subject.---E. J. F. Primrose, Mathematical Gazette

Topics

Frontmatter Publicly Available Download PDF	i
Preface Requires Authentication Unlicensed Licensed Download PDF	v
Contents Publicly Available Download PDF	vii
Chapter I. Tensor analysis Requires Authentication Unlicensed Licensed Download PDF	1
Chapter II. Introduction of a metric Requires Authentication Unlicensed Licensed Download PDF	34
Chapter III. Orthogonal ennuples Requires Authentication Unlicensed Licensed Download PDF	96
Chapter IV. The geometry of sub-spaces Requires Authentication Unlicensed Licensed Download PDF	143
Chapter V. Sub-spaces of a flat space Requires Authentication Unlicensed Licensed Download PDF	187
Chapter VI. Groups of motions Requires Authentication Unlicensed Licensed Download PDF	221
Appendices Requires Authentication Unlicensed Licensed Download PDF	252
Bibliography Requires Authentication Unlicensed Licensed Download PDF	289
Index Requires Authentication Unlicensed Licensed Download PDF	301