Riemannian Geometry
By Luther Pfahler Eisenhart
* Publisher: Princeton University Press
* Number Of Pages: 272
* Publication Date: 1997-10-13
* ISBN-10 / ASIN: 0691023530
* ISBN-13 / EAN: 9780691023533
Product Description:
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.
Summary: The best classical-style exposition of Riemannian Geometry.
Rating: 5
I bought the Russian translation of this book in 1954 and found that this is the best source of the Riemannian geometry, not only for a beginner (as I was at that time), but also for every specialist. Some items fully discussed there by L.P. Eisenhart were even rediscovered decades later --- and published another time as new results. This book is, of course, written in the old good traditional style, one will not find here, e.g., Cartan's forms, but it is really an everlasting treasure. Look also for the Continuous Groups of Transformations by the same author.
http://ifile.it/31vudp/eisenhart_l.p._riemannian_geometry__princeton__1949__l__t__158s_.djvu
