IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-3-642-17286-1_25.html
   My bibliography  Save this book chapter

Hyperbolic Geometry

In: Perspectives on Projective Geometry

Author

Listed:
  • Jürgen Richter-Gebert

    (TU München, Zentrum Mathematik (M10) LS Geometrie)

Abstract

Back to mathematics! This chapter is dedicated to several interesting topics in hyperbolic geometry. With our previous knowledge on the real projective plane RP2, on the complex projective line CP1, and of Cayley-Klein geometries we have an ideal departure point to explain several hyperbolic effects from an elegant and advanced standpoint. In particular, we will work out the relations between the Beltrami-Klein model and the Poincaré disk model. Compared to the general considerations in Chapters 20–23 we are now in a somewhat better situation. When we dealt with general Cayley-Klein geometries we spent a lot of our efforts on the treatment of case distinctions that arose from the various degrees of degeneracy of the fundamental conic. The algebraic structure became easier the less degenerate the fundamental conic was. Now we will deal only with one particular Cayley-Klein geometry, which in addition is nondegenerate.

Suggested Citation

  • Jürgen Richter-Gebert, 2011. "Hyperbolic Geometry," Springer Books, in: Perspectives on Projective Geometry, chapter 25, pages 483-503, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-17286-1_25
    DOI: 10.1007/978-3-642-17286-1_25
    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

    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:978-3-642-17286-1_25. 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.