Book Review: Riemannian geometry: A modern introduction

Abstract

2nd ed. This corrected and clarified second edition, including a new chapter on the Riemannian geometry of surfaces, provides an introduction to the geometry of curved spaces. Its main theme is the effect of the curvature of spaces on the usual notions of geometry, angles, lengths, areas, and volumes, and on those new notions and ideas motivated by curvature itself. Cover; Half-title; Series-title; Title; Copyright; Dedication; Contents; Preface to the Second Edition; Preface; I Riemannian Manifolds; II Riemannian Curvature; III Riemannian Volume; IV Riemannian Coverings; V Surfaces; VI Isoperimetric Inequalities (Constant Curvature); VII The Kinematic Density; VIII Isoperimetric Inequalities (Variable Curvature); IX Comparison and Finiteness Theorems; Hints and Sketches for Exercises; Bibliography; Author Index; Subject Index.