Riemannian geometry : a modern introduction / Isaac Chavel.Material type: TextSeries: Cambridge studies in advanced mathematics ; 98.Publication details: New York : Cambridge University Press, 2006. Edition: 2nd edDescription: 1 online resource (xvi, 471 pages) : illustrationsContent type: text Media type: computer Carrier type: online resourceISBN: 9780511221200; 0511221207; 0511219911; 9780511219917; 9780511219238; 0511219237; 9786610515936; 661051593X; 0511220324; 9780511220326Subject(s): Geometry, Riemannian | Geometry, Differential | MATHEMATICS -- Geometry -- Analytic | Geometry, Differential | Geometry, RiemannianGenre/Form: Electronic books. | Electronic books. | Electronic books. Additional physical formats: Print version:: Riemannian geometry.DDC classification: 516.3/73 LOC classification: QA649 | .C45 2006ebOnline resources: Click here to access online
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Includes bibliographical references (pages 449-464) and indexes.
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.
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.
Print version record.