DOI: 10.31801/cfsuasmas.1592170 ISSN: 1303-5991

Generalized Elastic Line, Differentials of Maps Connected with CNLSE via Conformal Derivative and Magnetic Curves for Darboux Frame

Nevin Ertuğ Gürbüz
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In this paper, we study generalized elastic lines via the intrinsic directional derivatives for the Darboux frame in $\mathbb{R}^{3}$. Subsequently, we investigate the congruences of surfaces associated with the Darboux frame in $\mathbb{R}^{3}$. Furthermore, we establish the Darboux conformal derivative equations and conformal magnetic curves for the Darboux frame in $\mathbb{R}^{3}$. Finally, we present formulas for conformal differentials of maps associated with the CNLSE for the Darboux frame in $\mathbb{R}^{3}$.

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