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: Riemannian manifolds
    sub title: an introduction to curvature
  name:
    name part: Lee, John M.
    name part: 1950-
    role:
      role term: creator
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  genre: bibliography
  genre: Electronic books.
  origin info:
    place:
      place term: nyu
    date issued: 1997
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: remote
    extent: 1 online resource (xv, 224 pages) : illustrations.
  abstract: This text is designed for a one-quarter or one-semester graduate couse in Riemannian geometry. It focuses on developing an intimate acquaintance with the geometric meaning of curvature and thereby introduces and demonstrates all the main technical tools needed for a more advanced course on Riemannian manifolds. The book begins with a careful treatment of the machinery of metrics, connections, and geodesics, and then introduces the Riemann curvature tensor, before moving on the submanifold theory, in order to give the curvature tensor a concrete quantitative interpretation. The remainder of the text is devoted to proving the four most fundamental theorems relating curvature and topology: the Gauss-Bonnet Theorem, the Cartan-Hadamard Theorem, Bonnet's Theorem, and a special case of the Cartan-Ambrose- Hicks Theorem. This unique volume will especially appeal to students by presenting a selective introduction to the main ides of the subject in an easily accessible way. The material is ideal for a single course, but broad enough to provide students with a firm foundation from which to pursue research or develop applications in Riemannian geometry and other fields that use its tools. Of special interest are the "exercises" and "problems" dispersed throughout the text. The exercises are carefully chosen and timed so as to give the reader opportunities to review material that hasjust been introduced, to practice working with the definitions, and to develop skills that are used later in the book. The problems that conclude the chapters are generally more difficult. They not only introduce new mateiral not covered in the body of the text, but they also provide the students with indispensable practice in using the.
  table of contents: Cover -- Preface -- Table of Contents -- 1. What Is Curvature? -- 2. Review of Tensors, Manifolds, and Vector Bundles -- 3. Definitions and Examples of Riemannian Metrics -- 4. Connections -- 5. Riemannian Geodesics -- 6. Geodesics and Distance -- 7. Curvature -- 8. Riemannian Submanifolds -- 9. The Gauss-Bonnet Theorem -- 10. Jacobi Fields -- 11. Curvature and Topology -- References.
  note: John M. Lee.
  note: Electronic resource.
  note: Includes bibliographical references (pages 209-211) and index.
  subject:
    topic: Riemannian manifolds
  subject:
    topic: Riemann, Variétés de
  subject:
    topic: MATHEMATICS
    topic: Geometry
    topic: Analytic
  subject:
    topic: Riemannian manifolds
  subject:
    topic: Riemann-vlakken
  subject:
    topic: Geometria diferencial
  classification: QA649 .L397 1997eb
  classification: 516.3/73
  classification: 31.52
  related item:
    title info:
      title: Riemannian manifolds
    name:
      name part: Lee, John M., 1950-
    origin info:
      publisher: New York : Springer, ©1997
    identifier: (DLC) 97014537
    identifier: (OCoLC)36800559
  related item:
    title info:
      title: Graduate texts in mathematics ; 176
  identifier: 0387227261
  identifier: 9780387227269
  identifier: 9780387982717
  identifier: 038798271X
  identifier: 0387983228
  identifier: EBL219515 eBook Library
  identifier: http://proxy.library.tamu.edu/login
  record info:
    record content source: N$T
    record creation date: 040331
    record change date: 20260422224817.0
    record identifier: in00003502272
    language of cataloging:
      language term: eng