02821nam a22003735i 4500978-3-540-77341-2cr nn 008mamaa100301s2008 gw : s :::: 0:eng d9783540773412ENGDEQA641-670516.36 (DDC 23)Online Resource : SpringerJost, Jürgen1956-Riemannian Geometry and Geometric AnalysisEBby Jürgen Jost.Fifth editionBerlin, Heidelberg,Springer2008.XIV, 590 p. 14 illus., 4 illus. in color.online resource.textonline resourceUniversitextFundamental Material -- De Rham Cohomology and Harmonic Differential Forms -- Parallel Transport, Connections, and Covariant Derivatives -- Geodesics and Jacobi Fields -- A Short Survey on Curvature and Topology: Symmetric Spaces and Kähler Manifolds -- Morse Theory and Floer Homology -- Harmonic Maps between Riemannian Manifolds -- Harmonic Maps from Riemann Surfaces -- Variational Problems from Quantum Field Theory -- Appendix A: Linear Elliptic Partial Differential Equations -- Appendix B: Fundamental Groups and Covering Spaces -- Bibliography -- Index.This established reference work continues to lead its readers to some of the hottest topics of contemporary mathematical research.This new edition introduces and explains the ideas of the parabolic methods that have recently found such a spectacular success in the work of Perelman at the examples of closed geodesics and harmonic forms. It also discusses further examples of geometric variational problems from quantum field theory, another source of profound new ideas and methods in geometry. From the reviews: "This book provides a very readable introduction to Riemannian geometry and geometric analysis. The author focuses on using analytic methods in the study of some fundamental theorems in Riemannian geometry, e.g., the Hodge theorem, the Rauch comparison theorem, the Lyusternik and Fet theorem and the existence of harmonic mappings. With the vast development of the mathematical subject of geometric analysis, the present textbook is most welcome. [..] The book is made more interesting by the perspectives in various sections." Mathematical Reviews"Online access is restricted to subscription institutions through IP address (only for SISSA internal users)Mathematics.Global differential geometry.Mathematical physics.Mathematics.Differential geometryMathematical and Computational Physics.SpringerLink (Online service)Universitexthttp://dx.doi.org/10.1007/978-3-540-77341-2