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

Year 2024, Volume: 7 Issue: To memory "Assoc. Prof. Dr. Zeynep AKDEMİRCİ ŞANLI", 158 - 174, 29.12.2024

Şerife Nevin Gürbüz

https://doi.org/10.33773/jum.1558660

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

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