Riemannian Geometry: A Modern Introduction

ISBN-13: 9780521853682 / Angielski / Twarda / 2006 / 488 str.

Isaac Chavel; B. Bollobas; W. Fulton

Opis

Requiring only an understanding of differentiable manifolds, Isaac Chavel covers introductory ideas followed by a selection of more specialized topics in this second edition. He provides a clearer treatment of many topics, with new proofs of some theorems and a new chapter on the Riemannian geometry of surfaces. Among the classical topics shown in a new setting is isoperimetric inequalities in curved spaces. Completely new themes created by curvature include the classical Rauch comparison theorem and its consequences in geometry and topology, and the interaction of microscopic behavior of the geometry with the macroscopic structure of the space.

Recenzje

'… I think that it is the best reference on Riemannian geometry available, especially for someone interested in isoperimetric problems. … an insightful modern perspective on topics of current research interest.' SIAM Review

Spis treści

1. Riemannian manifolds; 2. Riemannian curvature; 3. Riemannian volume; 4. Riemannian coverings; 5. Surfaces; 6. Isoperimetric inequalities (constant curvature); 7. The kinetic density; 8. Isoperimetric inequalities (variable curvature); 9. Comparison and finiteness theorems.