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Riemannian Geometry and Geometric Analysis

  • Textbook
  • © 2017

Overview

Authors:
  1. Jürgen Jost

    1. Max Planck Institute for Mathematics in the Sciences, Max Planck Society, Leipzig, Germany

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  • Continues to lead its readers to some of the hottest topics of contemporary research
  • Each chapter now includes additional basic exercises to test the reader’s understanding
  • Features new material on Ricci curvature

Part of the book series: Universitext (UTX)

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Table of contents (12 chapters)

  1. Front Matter

    Pages i-xiv
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  2. Chapter 1 Riemannian Manifolds

    • Jürgen Jost
    Pages 1-49

  3. Chapter 2 Lie Groups and Vector Bundles

    • Jürgen Jost
    Pages 51-114

  4. Chapter 3 The Laplace Operator and Harmonic Differential Forms

    • Jürgen Jost
    Pages 115-162

  5. Chapter 4 Connections and Curvature

    • Jürgen Jost
    Pages 163-232

  6. Chapter 5 Geometry of Submanifolds

    • Jürgen Jost
    Pages 233-249

  7. Chapter 6 Geodesics and Jacobi Fields

    • Jürgen Jost
    Pages 251-315

  8. A Short Survey on Curvature and Topology

    • Jürgen Jost
    Pages 317-325

  9. Chapter 7 Symmetric Spaces and Kähler Manifolds

    • Jürgen Jost
    Pages 327-390

  10. Chapter 8 Morse Theory and Floer Homology

    • Jürgen Jost
    Pages 391-487

  11. Chapter 9 Harmonic Maps Between Riemannian Manifolds

    • Jürgen Jost
    Pages 489-571

  12. Chapter 10 Harmonic Maps from Riemann Surfaces

    • Jürgen Jost
    Pages 573-630

  13. Chapter 11 Variational Problems from Quantum Field Theory

    • Jürgen Jost
    Pages 631-655

  14. Back Matter

    Pages 657-697
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Keywords

About this book

This 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 newmaterial, 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

Reviews

“The present volume ends with two appendices (on linear elliptic partial differential equations and topological results about fundamental groups and covering spaces) and a rich bibliography of 454 items, including some classical books and papers. All the material, written in a clear and precise style, is carefully developed, many examples supporting the understanding. In the reviewer’s opinion, this is an excellent book, a very useful addition to any good library.” (Gabriel Eduard Vilcu, zbMATH 1380.53001, 2018)

Authors and Affiliations

  • Max Planck Institute for Mathematics in the Sciences, Max Planck Society, Leipzig, Germany

    Jürgen Jost

About the author

Jürgen Jost is Codirector of the Max Planck Institute for Mathematics in the Sciences in Leipzig, Germany, an Honorary Professor at the Department of Mathematics and Computer Sciences at Leipzig University, and an External Faculty Member of the Santa Fe Institute for the Sciences of Complexity, New Mexico, USA.

He is the author of a number of further Springer textbooks including Postmodern Analysis (1997, 2002, 2005), Compact Riemann Surfaces (1997, 2002, 2006), Partial Differential Equations (2002, 2007, 2013), Differentialgeometrie und Minimalflächen (1994, 2007, 2014, with J. Eschenburg), Dynamical Systems (2005), Mathematical Concepts (2015), as well as several research monographs, such as Geometry and Physics (2009), and many publications in scientific journals.





Bibliographic Information

  • Book Title: Riemannian Geometry and Geometric Analysis

  • Authors: Jürgen Jost

  • Series Title: Universitext

  • DOI: https://doi.org/10.1007/978-3-319-61860-9

  • Publisher: Springer Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer International Publishing AG 2017

  • Softcover ISBN: 978-3-319-61859-3Published: 23 October 2017

  • eBook ISBN: 978-3-319-61860-9Published: 13 October 2017

  • Series ISSN: 0172-5939

  • Series E-ISSN: 2191-6675

  • Edition Number: 7

  • Number of Pages: XIV, 697

  • Number of Illustrations: 15 b/w illustrations, 4 illustrations in colour

  • Additional Information: Originally published by Springer-Verlag Berlin Heidelberg, 1995, 1998, 2002, 2005, 2008, 2011

  • Topics: Differential Geometry, Theoretical, Mathematical and Computational Physics

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