IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i8p1820-d1121165.html
   My bibliography  Save this article

On Translation Curves and Geodesics in Sol 1 4

Author

Listed:
  • Zlatko Erjavec

    (Faculty of Organization and Informatics, University of Zagreb, HR-42000 Varaždin, Croatia)

  • Marcel Maretić

    (Faculty of Organization and Informatics, University of Zagreb, HR-42000 Varaždin, Croatia)

Abstract

A translation curve in a homogeneous space is a curve such that for a given unit vector at the origin, translation of this vector is tangent to the curve in its every point. Translation curves coincide with geodesics in most Thurston spaces, but not in twisted product Thurston spaces. Moreover, translation curves often seem more intuitive and simpler than geodesics. In this paper, we determine translation curves in Sol 1 4 space. Their curvature properties are discussed and translation spheres are presented. Finally, characterization of geodesics in Sol 1 4 space is given.

Suggested Citation

  • Zlatko Erjavec & Marcel Maretić, 2023. "On Translation Curves and Geodesics in Sol 1 4," Mathematics, MDPI, vol. 11(8), pages 1-10, April.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:8:p:1820-:d:1121165
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/8/1820/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/8/1820/
    Download Restriction: no
    ---><---

    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:gam:jmathe:v:11:y:2023:i:8:p:1820-:d:1121165. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.