LEADER 04319nam 22005655 450 001 9910254285803321 005 20200706061655.0 010 $a3-319-61860-1 024 7 $a10.1007/978-3-319-61860-9 035 $a(CKB)4100000000881619 035 $a(DE-He213)978-3-319-61860-9 035 $a(MiAaPQ)EBC6312488 035 $a(MiAaPQ)EBC5610936 035 $a(Au-PeEL)EBL5610936 035 $a(OCoLC)1007152776 035 $a(PPN)220125279 035 $a(EXLCZ)994100000000881619 100 $a20171013d2017 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aRiemannian Geometry and Geometric Analysis /$fby Jürgen Jost 205 $a7th ed. 2017. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2017. 215 $a1 online resource (XIV, 697 p. 19 illus., 4 illus. in color.) 225 1 $aUniversitext,$x0172-5939 311 $a3-319-61859-8 320 $aIncludes bibliographical references and index. 327 $a1 Riemannian Manifolds -- 2 Lie Groups and Vector Bundles -- 3 The Laplace Operator and Harmonic Differential Forms -- 4 Connections and Curvature -- 5 Geometry of Submanifolds -- 6 Geodesics and Jacobi Fields -- A Short Survey on Curvature and Topology -- 7 Symmetric Spaces and Kähler Manifolds -- 8 Morse Theory and Floer Homology -- 9 Harmonic Maps between Riemannian Manifolds -- 10 Harmonic Maps from Riemann Surfaces -- 11 Variational Problems from Quantum Field Theory -- A Linear Elliptic Partial Differential Equations -- B Fundamental Groups and Covering Spaces -- Bibliography -- Index. 330 $aThis established reference work continues to provide its readers with a gateway to some of the most interesting developments in contemporary geometry. It offers insight into a wide range of topics, including fundamental concepts of Riemannian geometry, such as geodesics, connections and curvature; the basic models and tools of geometric analysis, such as harmonic functions, forms, mappings, eigenvalues, the Dirac operator and the heat flow method; as well as the most important variational principles of theoretical physics, such as Yang-Mills, Ginzburg-Landau or the nonlinear sigma model of quantum field theory. The present volume connects all these topics in a systematic geometric framework. At the same time, it equips the reader with the working tools of the field and enables her or him to delve into geometric research. The 7th edition has been systematically reorganized and updated. Almost no page has been left unchanged. It also includes new material, for instance on symplectic geometry, as well as the Bishop-Gromov volume growth theorem which elucidates the geometric role of Ricci curvature. From the reviews: ?This book provides a very readable introduction to Riemannian geometry and geometric analysis... With the vast development of the mathematical subject of geometric analysis, the present textbook is most welcome.? Mathematical Reviews ?For readers familiar with the basics of differential geometry and some acquaintance with modern analysis, the book is reasonably self-contained ? The book succeeds very well in laying out the foundations of modern Riemannian geometry and geometric analysis. It introduces a number of key techniques and provides a representative overview of the field.? Monatshefte für Mathematik. 410 0$aUniversitext,$x0172-5939 606 $aDifferential geometry 606 $aMathematical physics 606 $aDifferential Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M21022 606 $aTheoretical, Mathematical and Computational Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P19005 615 0$aDifferential geometry. 615 0$aMathematical physics. 615 14$aDifferential Geometry. 615 24$aTheoretical, Mathematical and Computational Physics. 676 $a516.373 700 $aJost$b Jürgen$4aut$4http://id.loc.gov/vocabulary/relators/aut$054734 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910254285803321 996 $aRiemannian geometry and geometric analysis$982994 997 $aUNINA