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:
    non sort: An
    title: Introduction to Riemann-Finsler Geometry
  name:
    name part: Bao, D.
    role:
      role term: creator
  name:
    name part: Chern, S.-S.
  name:
    name part: Shen, Z.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  genre: Electronic books.
  origin info:
    place:
      place term: nyu
    date issued: 2000
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: remote
    extent: 1 online resource (XX, 431 pages 20 illustrations)
  abstract: In Riemannian geometry, measurements are made with both yardsticks and protractors. These tools are represented by a family of inner-products. In Riemann-Finsler geometry (or Finsler geometry for short), one is in principle equipped with only a family of Minkowski norms. So ardsticks are assigned but protractors are not. With such a limited tool kit, it is natural to wonder just how much geometry one can uncover and describe? It now appears that there is a reasonable answer. Finsler geometry encompasses a solid repertoire of rigidity and comparison theorems, most of them founded upon a fruitful analogue of the sectional curvature. There is also a bewildering array of explicit examples, illustrating many phenomena which admit only Finslerian interpretations. This book focuses on the elementary but essential items among these results. Much thought has gone into making the account a teachable one.
  table of contents: From the contents: Finsler methods and the fundamentals of Minkowski norms -- The Chern connection -- Curvature and Schur's Lemma -- Finsler surfaces and a generalized Gauss-Bonnet theorem -- Variations of arc length, Jacobi fields, and the effect of curvature -- The Gauss lemma and the Hopf-Rinow theorem -- The index form and the Bonnet-Myers theorem -- The cut and conjugate loci, and Synge's theorem -- The Cartan-Hadamard theorem and Rauch's first theorem -- Berwald spaces and Szabo's theorem for Berwald spaces -- Randers spaces and a theorem from the Japanese school -- Constant flag curvature spaces, and ther Andar-Zadeh theorem -- Riemannian manifolds and two theorems of Hopf's -- Minkowski spaces, the theorems of Dickie and Brickell.
  note: by D. Bao, S.-S. Chern, Z. Shen.
  note: Electronic resource.
  subject:
    topic: Geometry, Riemannian
  subject:
    topic: Finsler spaces
  subject:
    topic: Finsler spaces
  subject:
    topic: Geometry, Riemannian
  classification: QA649
  classification: 516.3/73
  related item:
    title info:
      title: Graduate texts in mathematics ; 200
  identifier: 9781461212683 (electronic bk.)
  identifier: 1461212685 (electronic bk.)
  identifier: http://proxy.library.tamu.edu/login
  record info:
    record content source: I9W
    record creation date: 121227
    record change date: 20260420205725.3
    record identifier: in00003547062
    language of cataloging:
      language term: eng