GEOMETRIC PHASES, MAGNETIC CURVES FOR DARBOUX FRAMES ON LIGHTLIKE AND TIMELIKE SURFACES

Authors : Şerife Nevin Gürbüz

Pages : 158-174

Doi:10.33773/jum.1558660

View : 95 | Download : 136

Publication Date : 2024-12-29

Article Type : Research Paper

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.
Keywords : Geometric phase, Darboux frame, magnetic curves