Focal Surfaces Connected with VFF for Type 1-PAF in $\mathbb{E}{^{3}}$

Abstract

In this paper, we obtain vortex filament flow (VFF) surfaces for three classes according to Type 1-PAF in Euclidean 3-space $\mathbb{E}{^{3}}$. Additionally, we obtain the first and second fundamental forms, Gauss and mean curvatures of focal surfaces generated by vortex filament flow surfaces in Euclidean 3-space $\mathbb{E}{^{3}}$. Furthermore , we present focal surfaces generated by vortex filament flow for three classes according Type 1-PAF in Euclidean 3-space $\mathbb{E}{^{3}}$. Finaly, we provide examples related to focal surfaces generated by vortex filament flow surfaces for three classes according Type 1-PAF in Euclidean 3-space $\mathbb{E}{^{3}}$.

Keywords

• VFF
• Type 1-PAF
• Euclidean space

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