Riemannian geometry
Subtitle: a modern introduction
By: Isaac Chavel.
Series: Cambridge tracts in mathematics ;; 108
Publisher: Cambridge University Press
Published: 1993
Place of publication: Cambridge [England]; New York
Language: eng
Number of pages: 386
Subjects: Geometry, Riemannian.
Description: This book provides an introduction to Riemannian geometry, the geometry of curved spaces. Its main theme is the effect of the curvature of these spaces on the usual notions of geometry - distances, areas, and volumes - and on those new notions and ideas motivated by curvature itself. Among the more specialized classical topics in a new setting are volume-comparison theorems, and isoperimetric inequalities - the interplay of curvature with volume of sets and the areas of their boundaries.

Completely new themes created by curvature include the interaction of microscopic behavior 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, here treated in book form for the first time. Also featured is a nontraditional Notes and Exercises section for each chapter, to develop and enrich the readers appetite for and appreciation of the subject.
Notes: Includes bibliographical references (p. 371-381) and index.