IDEAS home Printed from https://ideas.repec.org/p/cor/louvco/2004007.html
   My bibliography  Save this paper

Invariants in the Riemannian geometry of convex sets

Author

Listed:
  • HILDEBRAND, Roland

Abstract

In this contribution we study some aspects of the Riemannian geometry induced on a convex set by a barrier function of the set. Using Noether's theorem, we link the symmetries of the set to invariants of the geodesic flow. This allows to lower the dimension of the differential system defining the geodesics and gives insights in the structure of the geodesic flow, specifically on the configuration of geodesic submanifolds. We use the developed apparatus to completely integrate the geodesicequations for the convex hulls of the sphere, the paraboloid, the hyperboloid and the standard symmetricc ones and to obtain explicit formulae for the geodesics on these sets.

Suggested Citation

  • HILDEBRAND, Roland, 2004. "Invariants in the Riemannian geometry of convex sets," LIDAM Discussion Papers CORE 2004007, Universit√© catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  • Handle: RePEc:cor:louvco:2004007
    as

    Download full text from publisher

    File URL: https://uclouvain.be/en/research-institutes/immaq/core/dp-2004.html
    Download Restriction: no
    ---><---

    More about this item

    Keywords

    Riemannian geometry; barrier function; convexity; symmetry;
    All these keywords.

    JEL classification:

    • C69 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Other

    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:cor:louvco:2004007. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: . General contact details of provider: https://edirc.repec.org/data/coreebe.html .

    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: Alain GILLIS (email available below). General contact details of provider: https://edirc.repec.org/data/coreebe.html .

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.