@article{article_1558660, title={GEOMETRIC PHASES, MAGNETIC CURVES FOR DARBOUX FRAMES ON LIGHTLIKE AND TIMELIKE SURFACES}, journal={Journal of Universal Mathematics}, volume={7}, pages={158–174}, year={2024}, DOI={10.33773/jum.1558660}, author={Gürbüz, Şerife Nevin}, keywords={Geometric phase, Darboux frame, magnetic curves}, abstract={In this paper, we obtain ^{ND}E_{T} for null Darboux frame on timelike surface and derive V-magnetic curves for null Darboux frame on a timelike surface in the T-lines direction. Also, we present ^{¹GD}E_{T}, ^{^{²GD }E_{T} for 1GDF, 2GDF on lightlike surfaces in the tangential direction. Later, we present μ, U-magnetic curves for 1GDF on lightlike surfaces in the T-lines direction. We obtain geometric phase in μ-lines direction for 1GDF on lightlike surface. Finally, we obtain μ,U-magnetic curves in the μ,U-lines direction for 1GDF on lightlike surfaces.}, number={To memory "Assoc. Prof. Dr. Zeynep AKDEMİRCİ ŞANLI"}, publisher={Gökhan ÇUVALCIOĞLU}