IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i23p3121-d694466.html
   My bibliography  Save this article

Canonical Coordinates and Natural Equation for Lorentz Surfaces in R 1 3

Author

Listed:
  • Krasimir Kanchev

    (Department of Mathematics and Informatics, Todor Kableshkov University of Transport, 158 Geo Milev Str., 1574 Sofia, Bulgaria)

  • Ognian Kassabov

    (Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str. bl. 8, 1113 Sofia, Bulgaria)

  • Velichka Milousheva

    (Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str. bl. 8, 1113 Sofia, Bulgaria)

Abstract

We consider Lorentz surfaces in R 1 3 satisfying the condition H 2 − K ≠ 0 , where K and H are the Gaussian curvature and the mean curvature, respectively, and call them Lorentz surfaces of general type. For this class of surfaces, we introduce special isotropic coordinates, which we call canonical, and show that the coefficient F of the first fundamental form and the mean curvature H , expressed in terms of the canonical coordinates, satisfy a special integro-differential equation which we call a natural equation of the Lorentz surfaces of a general type. Using this natural equation, we prove a fundamental theorem of Bonnet type for Lorentz surfaces of a general type. We consider the special cases of Lorentz surfaces of constant non-zero mean curvature and minimal Lorentz surfaces. Finally, we give examples of Lorentz surfaces illustrating the developed theory.

Suggested Citation

  • Krasimir Kanchev & Ognian Kassabov & Velichka Milousheva, 2021. "Canonical Coordinates and Natural Equation for Lorentz Surfaces in R 1 3," Mathematics, MDPI, vol. 9(23), pages 1-12, December.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:23:p:3121-:d:694466
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/23/3121/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/23/3121/
    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:9:y:2021:i:23:p:3121-:d:694466. 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.