Djordjevic, JelenaNesovic, EmilijaÖztürk, Ufuk2023-08-142023-08-142023DJORDJEVIC, J., NESOVIC, E., & ÖZTÜRK, U. (2023). On generalized Darboux frame of a spacelike curve lying on a lightlike surface in Minkowski space $\mathbb {E}^{3} _ {1} $. Turkish Journal of Mathematics, 47(2), 883-897.1300-00981303-6149http://dx.doi.org/10.55730/1300-0098.3399https://hdl.handle.net/20.500.12491/11509Serbian Ministry of Education, Science and Technological Development(Ministry of Education, Science & Technological Development, Serbia)In this paper we introduce generalized Darboux frame of a spacelike curve alpha lying on a lightlike surface in Minkowski space E31 . We prove that alpha has two such frames and obtain generalized Darboux frame's equations. We find the relations between the curvature functions kg, kn , tau g of alpha with respect to its Darboux frame and the curvature functions k similar to g, k similar to n , tau similar to g with respect to generalized Darboux frames. We show that such frames exist along a spacelike straight line lying on a ruled surface which is not entirely lightlike, but contains some lightlike points. We define lightlike ruled surfaces on which the tangent and the binormal indicatrix of a null Cartan curve are the principal curvature lines having tau similar to g = 0 and give some examples.eninfo:eu-repo/semantics/openAccessGeneralized Darboux FrameSpacelike CurveDarboux FrameLightlike SurfaceMinkowski SpaceHypersurfaceArticle10.55730/1300-0098.33994728838972-s2.0-85151915561Q21160529WOS:000986888900031Q2