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

Krasimir Kanchev, Ognian Kassabov and Velichka Milousheva
Additional contact information
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

Mathematics, 2021, vol. 9, issue 23, 1-12

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.

Keywords: Lorentz surfaces; pseudo-Euclidean space; canonical coordinates; natural equations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/9/23/3121/pdf (application/pdf)
https://www.mdpi.com/2227-7390/9/23/3121/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:9:y:2021:i:23:p:3121-:d:694466

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().