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: Morse index of minimal submanifolds
  name:
    name part: Urbano, Francisco
    name part: (Mathematician)
    role:
      role term: creator
    role:
      role term: author.
  type of resource: text
  genre: bibliography
  origin info:
    place:
      place term: riu
    date issued: 2025
    copyright date: 2025
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: print
    extent: xiv, 293 pages : illustrations (some color) ; 26 cm.
  abstract: This book provides a systematic treatment of the main results on the Morse index of minimal submanifolds of Riemannian manifolds. After an introductory chapter reviewing the necessary material, this book provides a survey of the basic properties of the Morse index, as well as a large number of examples of minimal submanifolds with the corresponding calculation of their Morse index. The analysis of minimal submanifolds and their index in the cases when the ambient manifold is the Euclidean space, sphere, real and complex projective spaces are analyzed in detail. Many other classes of ambient varieties are also studied. The text also includes some of the main open problems in the theory. Potential readers of this book are graduate students and researchers in geometric analysis.
  table of contents: 1. Foundations -- 2. Variation formulas. stability, index and nullity -- 3. Complete minimal submanifolds of non-negatively curved Riemannian manifolds -- 4. Index of minimal submanifolds of Euclidean spaces -- 5. Index of minimal submanifolds of spheres, real projective spaces, product of spheres and elliptic Berger spheres -- Index of minimal submanifolds of Kahler manifolds.
  note: Francisco Urbano.
  note: Includes bibliographical references and indexes.
  subject:
    topic: Minimal submanifolds
  subject:
    topic: Morse theory
  classification: QA649 .U73 2025
  classification: 516.3/6
  related item:
    title info:
      title: Mathematical surveys and monographs ; no. 292
  identifier: 1470480212
  identifier: 9781470480219
  identifier: 9781470481674
  identifier: 2025176008
  record info:
    record content source: DLC
    record creation date: 250715
    record change date: 20251015192401.2
    record identifier: in00005665503