IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-3-642-18245-7_4.html

Riemann’s Blueprints for Architecture in Myriad Dimensions

In: A Panoramic View of Riemannian Geometry

Author

Listed:
  • Marcel Berger

    (Institut des Hautes Études Scientifiques IHES)

Abstract

As we said in chapter 2, Riemann’s construction of the Riemannian manifold consisted first in building the foundation of the smooth manifold. He then established on that foundation the concept of a Riemannian metric. In the first two sections we will present smooth manifolds, and thereafter define Riemannian metrics. The notion of smooth manifold is at the same time extremely natural and quite hard to define correctly. This notion started with Riemann in 1854 and was widely used. Hermann Weyl was the first to lay down solid foundations for this notion in 1923. The definition became completely clear in the famous article Whitney 1936 [1259].

Suggested Citation

  • Marcel Berger, 2003. "Riemann’s Blueprints for Architecture in Myriad Dimensions," Springer Books, in: A Panoramic View of Riemannian Geometry, chapter 4, pages 143-218, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-18245-7_4
    DOI: 10.1007/978-3-642-18245-7_4
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:sprchp:978-3-642-18245-7_4. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.