Riemannian Geometry and Geometric Analysis (7th Edition) (Universitext)

December 8, 2020
Riemannian Geometry and Geometric Analysis (7th Edition) (Universitext)

Continues to lead its readers to some of the hottest topics ofcontemporary researchEach chapter now includes additional basic exercises to testthe reader’s understandingFeatures new material on Ricci curvature——————————This established reference work continues to provide its readerswith a gateway to some of the most interesting developments incontemporary geometry. It offers insight into a wide range oftopics, including fundamental concepts of Riemannian geometry, suchas geodesics, connections and curvature; the basic models and toolsof geometric analysis, such as harmonic functions, forms, mappings,eigenvalues, the Dirac operator and the heat flow method; as wellas the most important variational principles of theoreticalphysics, such as Yang-Mills, Ginzburg-Landau or the nonlinear sigmamodel of quantum field theory. The present volume connects allthese topics in a systematic geometric framework. At the same time,it equips the reader with the working tools of the field andenables her or him to delve into geometric research.The 7th edition has been systematically reorganized and updated.Almost no page has been left unchanged. It also includes newmaterial, for instance on symplectic geometry, as well as theBishop-Gromov volume growth theorem which elucidates the geometricrole of Ricci curvature.From the reviews:“This book provides a very readable introduction to Riemanniangeometry and geometric analysis... With the vast development of themathematical subject of geometric analysis, the present textbook ismost welcome.” Mathematical Reviews“For readers familiar with the basics of differential geometryand some acquaintance with modern analysis, the book is reasonablyself-contained. The book succeeds very well in laying out thefoundations of modern Riemannian geometry and geometric analysis.It introduces a number of key techniques and provides arepresentative overview of the field.” Monatshefte fürMathematik