IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-3-642-25588-5_17.html
   My bibliography  Save this book chapter

Rotation Hypersurfaces in Spaces of Constant Curvature

In: Manfredo P. do Carmo – Selected Papers

Author

Listed:
  • M. do Carmo

    (lnstituto de Matemática Pura e Aplicada (IMPA))

  • M. Dajczer

    (lnstituto de Matemática Pura e Aplicada (IMPA))

Abstract

Rotation hypersurfaces in spaces of constant curvature are defined and their principal curvatures are computed. A local characterization of such hypersurfaces, with dimensions greater than two, is given in terms of principal curvatures. Some special cases of rotation hypersurfaces, with constant mean curvature, in hyperbolic space are studied. In particular, it is shown that the well-known conjugation between the helicoid and the catenoid in euclidean three-space extends naturally to hyperbolic three-space H3 ; in the latter case, catenoids are of three different types and the explicit correspondence is given. It is also shown that there exists a family of simply-connected, complete, embedded, nontotally geodesic stable minimal surfaces in H3.

Suggested Citation

  • M. do Carmo & M. Dajczer, 2012. "Rotation Hypersurfaces in Spaces of Constant Curvature," Springer Books, in: Keti Tenenblat (ed.), Manfredo P. do Carmo – Selected Papers, edition 127, pages 195-219, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-25588-5_17
    DOI: 10.1007/978-3-642-25588-5_17
    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:978-3-642-25588-5_17. 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.