Riemannian Geometry: A Modern Introduction (Cambridge Tracts in Mathematics, Series Number 108) - Softcover

Chavel, Isaac

Softcover

ISBN 10: 0521485789 ISBN 13: 9780521485784

Publisher: Cambridge University Press, 1995

Synopsis

This book provides an introduction to Riemannian geometry, the geometry of curved spaces. As such, its main theme is the effect of the curvature of these spaces on the usual notions of geometry - angles, lengths, areas and volumes - and those new notions and ideas motivated by curvature itself. Among the specialized classical topics in this new setting is isoperimetric inequalities, that is, the interplay of curvature with the volume of sets and the areas of their boundaries. Completely new themes, created by curvature, include local versus global geometric properties, that is, the interaction of the microscopic behaviour of the geometry with the macroscopic structure of the space. After considering those topics which would form the core of an introductory course, the book emphasizes more specialized topics which have yet to be treated in book form. Also featured is an ambitious and non-traditional notes and exercises section for each chapter, to develop and enrich the reader's appetite for, and appreciation of the subject.

About this title

Book Description

This book provides an introduction to Riemannian geometry, the geometry of curved spaces. It explores the effect of the curvature of these spaces on the usual notions of geometry, and those new notions and ideas motivated by curvature itself.

Edition details

• Publisher: Cambridge University Press
• Publication date: 1995
• Language: English
• ISBN 10: 0521485789
• ISBN 13: 9780521485784
• Binding: Paperback
• Number of pages: 400