Author: Luther Pfahler Eisenhart
Publisher: Princeton University Press
Keywords: geometry, riemannian
Number of Pages: 272
Published: 1997-10-13
List price: $65.00
ISBN-10: 0691023530
ISBN-13: 9780691023533

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 re

Author: Marcel Berger
Publisher: Springer
Keywords: geometry, riemannian, view, panoramic
Number of Pages: 875
Published: 2003-08-08
List price: $69.95
ISBN-10: 3540653171
ISBN-13: 9783540653172

Riemannian geometry has today become a vast and important subject. This new book of Marcel Berger sets out to introduce readers to most of the living topics of the field and convey them quickly to the main results known to date. These results are stated without detailed proofs but the main ideas involved are described and motivated. This enables the reader to obtain a sweeping panoramic view of almost the entirety of the field. However, since a Riemannian manifold is, even initially, a subtle object, appealing to highly non-natural concepts, the first three chapters devote themselves to introd

Author: Jürgen Jost
Publisher: Springer
Keywords: universitext, analysis, geometric, geometry, riemannian
Number of Pages: 588
Published: 2008-04-28
List price: $69.95
ISBN-10: 3540773401
ISBN-13: 9783540773405

This established reference work continues to lead its readers to some of the hottest topics of contemporary mathematical research.This new edition introduces and explains the ideas of the parabolic methods that have recently found such a spectacular success in the work of Perelman at the examples of closed geodesics and harmonic forms. It also discusses further examples of geometric variational problems from quantum field theory, another source of profound new ideas and methods in geometry. From the reviews "This book provides a very readable introduction to Riemannian geometry and geometric a

Authors:Manfredo P. Carmo,  Francis Flaherty,
Publisher: Birkhäuser Bosto
Keywords: geometry, riemannian
Number of Pages: 320
Published: 1992-01-01
List price: $54.95
ISBN-10: 0817634908
ISBN-13: 9780817634902

This text has been adopted at: University of Pennsylvania, Philadelphia University of Connecticut, Storrs Duke University, Durham, NC California Institute of Technology, Pasadena University of Washington, Seattle Swarthmore College, Swarthmore, PA University of Chicago, IL University of Michigan, Ann Arbor "In the reviewer’s opinion, this is a superb book which makes learning a real pleasure." - Revue Romaine de Mathematiques Pures et Appliquees "This main-stream presentation of differential geometry serves well for a course on Riemannian geometry, and it is complemented by many annotate

Author: Takashi Sakai
Publisher: American Mathematical Society
Keywords: monographs, mathematical, translations, geometry, riemannian
Number of Pages: 358
Published: 1996-05-01
List price: $124.00
ISBN-10: 0821802844
ISBN-13: 9780821802847

This volume is an English translation of Sakai’s textbook on Riemannian geometry which was originally written in Japanese and published in 1992. The author’s intent behind the original book was to provide to advanced undergraduate and graduate students an introduction to modern Riemannian geometry that could also serve as a reference. The book begins with an explanation of the fundamental notion of Riemannian geometry. Special emphasis is placed on understandability and readability, to guide students who are new to this area. The remaining chapters deal with various topics in Riema

Author: Peter Petersen
Publisher: Springer
Keywords: mathematics, texts, graduate, geometry, riemannian
Number of Pages: 456
Published: 1997-11-07
List price: $79.95
ISBN-10: 0387982124
ISBN-13: 9780387982120

This book is meant for a one year course in Riemannian Geometry. The approach the author has taken deviates in some ways from the standard path. Instead of discussing variational calculus, the author introduces a more elementary approach which simply uses standard calculus together with some techniques from differential equations. This book will appeal to readers with a knowledge of standard manifold theory, including such topics as tensors and Stoke’s theorem. Scattered throughout the text is a variety of exercises which will help the readers to deepen their understanding of the

Author: Peter Petersen
Publisher: Springer
Keywords: mathematics, texts, graduate, geometry, riemannian
Number of Pages: 408
Published: 2006-08-09
List price: $64.95
ISBN-10: 0387292462
ISBN-13: 9780387292465

Intended for a one year course, this volume serves as a single source, introducing students to the important techniques and theorems, while also containing enough background on advanced topics to appeal to those students wishing to specialize in Riemannian geometry. This is one of the few works to combine both the geometric parts of Riemannian geometry and the analytic aspects of the theory, while also presenting the most up-to-date research. This book will appeal to readers with a knowledge of standard manifold theory, including such topics as tensors and Stokes theorem. Various exercises are