Altın, MustafaKazan, AhmetKaradağ, H. Bayram2024-08-042024-08-0420201307-5624https://doi.org/10.36890/iejg.599817https://search.trdizin.gov.tr/yayin/detay/412532https://hdl.handle.net/11616/89097In this study, firstly we give the weighted curvatures of non-null planar curves in Lorentz-Minkowski space with density eax2+by2and obtain the planar curves whose weighted curvaturesvanish in this space under the condition that the constants a and b are not zero at the same time.After giving the Frenet vectors of the non-null planar curves with zero weighted curvature inLorentz-Minkowski space with density eax2, we create the Smarandache curves of them. With theaid of these curves and their Smarandache curves, we get the ruled surfaces whose base curvesare non-null curves of which vanishing weighted curvature and ruling curves are Smarandachecurves of them. Followingly, we give some characterizations for these ruled surfaces by obtainingthe mean and Gaussian curvatures, distribution parameters and striction curves of them. Also,rotational surfaces which are generated by non-null planar curves with zero weighted curvaturesin Lorentz-Minkowski space E31 with density eax2+by2are studied under the condition that theconstants a and b are not zero at the same time. We draw the graphics of the obtained surfaces.eninfo:eu-repo/semantics/openAccessArticle132112910.36890/iejg.599817412532