Geometry - General & Miscellaneous

Riemannian Geometry: A Modern Introduction

Name: Riemannian Geometry: A Modern Introduction
Author: Isaac Chavel
ISBN: 9780521619547

by Isaac Chavel

Available on Bookshop Write a review

Books.org participates in affiliate programs including Bookshop.org and the Amazon Services LLC Associates Program. We may earn a commission from qualifying purchases made through links on this page, at no additional cost to you.

Overview

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.

Synopsis

This corrected and clarified second edition includes a new chapter on the Riemannian geometry of surfaces.

About the Author, Isaac Chavel

Isaac Chavel is Professor of Mathematics at The City College of the City University of New York. He received his Ph.D. in Mathematics from Yeshiva University under the direction of Professor Harry E. Rauch. He has published in international journals in the areas of differential geometry and partial differential equations, especially the Laplace and heat operators on Riemannian manifolds. His other books include Eigenvalues in Riemannian Geometry, Academic Press, 1984, and Isoperimetric Inequalities: Differential Geometric and Analytic Perspectives, Cambridge U. Press,
2001. He has been teaching at The City College of the City University of New York since 1970, and has been a member of the doctoral program of the City University of New York since
1976. He is a member of the American Mathematical Society.