Spacelike Curves on Lightlike NLS Surfaces Using Generalized Darboux Triads

Year 2025, Issue: 53, 1 - 13, 31.12.2025

Muradiye Çimdiker Aslan

https://doi.org/10.53570/jnt.1745842

https://izlik.org/JA23ND97ZD

Abstract

This study first investigates spacelike curves lying on a lightlike Nonlinear Schrödinger (NLS) surface in $3$-dimensional Minkowski space $E_{1}^{3}$. It then derives the time evolution of these curves using the first and second types of generalized Darboux triads defined along the $T$-direction. Within this framework, this paper obtains the angular momentum and the vortex filament equation. Furthermore, it calculates the first and second fundamental form components of the surface to determine its mean and Gaussian curvatures. Finally, the present study constructs the recursion and normalization operators associated with the geometric evolution.

Keywords

Vortex filament equation , NLS surfaces , recursion and normalization operators , generalized Darboux triads

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