rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Introduction to Riemannian Manifolds
  name:
    name part: Lee, John M.
    role:
      role term: creator
    role:
      role term: author.
    role:
      role term: aut
    role:
      role term: http://id.loc.gov/vocabulary/relators/aut
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: gw
    date issued: 2018
    edition: 2nd ed. 2018.
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XIII, 437 p. 210 illus. online resource.
  abstract: This textbook is designed for a one or two semester graduate course on Riemannian geometry for students who are familiar with topological and differentiable manifolds. The second edition has been adapted, expanded, and aptly retitled from Lee's earlier book, Riemannian Manifolds: An Introduction to Curvature. Numerous exercises and problem sets provide the student with opportunities to practice and develop skills; appendices contain a brief review of essential background material. While demonstrating the uses of most of the main technical tools needed for a careful study of Riemannian manifolds, this text focuses on ensuring that the student develops an intimate acquaintance with the geometric meaning of curvature. The reasonably broad coverage begins with a treatment of indispensable tools for working with Riemannian metrics such as connections and geodesics. Several topics have been added, including an expanded treatment of pseudo-Riemannian metrics, a more detailed treatment of homogeneous spaces and invariant metrics, a completely revamped treatment of comparison theory based on Riccati equations, and a handful of new local-to-global theorems, to name just a few highlights. Reviews of the first edition: Arguments and proofs are written down precisely and clearly. The expertise of the author is reflected in many valuable comments and remarks on the recent developments of the subjects. Serious readers would have the challenges of solving the exercises and problems. The book is probably one of the most easily accessible introductions to Riemannian geometry. (M.C. Leung, MathReview) The book's aim is to develop tools and intuition for studying the central unifying theme in Riemannian geometry, which is the notion of curvature and its relation with topology. The main ideas of the subject, motivated as in the original papers, are introduced here in an intuitive and accessible way...The book is an excellent introduction designed for a one-semester graduate course, cont…
  table of contents: Preface -- 1. What Is Curvature? -- 2. Riemannian Metrics -- 3. Model Riemannian Manifolds -- 4. Connections -- 5. The Levi-Cevita Connection -- 6. Geodesics and Distance -- 7. Curvature -- 8. Riemannian Submanifolds -- 9. The Gauss-Bonnet Theorem -- 10. Jacobi Fields -- 11. Comparison Theory -- 12. Curvature and Topology -- Appendix A: Review of Smooth Manifolds -- Appendix B: Review of Tensors -- Appendix C: Review of Lie Groups -- References -- Notation Index -- Subject Index.
  note: by John M. Lee.
  subject:
    topic: Differential geometry
  subject:
    topic: Differential Geometry
  classification: QA641-670
  classification: 516.36
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Graduate Texts in Mathematics, 176
  identifier: 9783319917559
  identifier: https://doi.org/10.1007/978-3-319-91755-9
  record info:
    record creation date: 190102
    record change date: 20191028162641.0
    record identifier: 978-3-319-91755-9