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

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Hagia Sophia Journal of Geometry
Cilt: 7 Sayı: 1
Focal Surfaces Connected with VFF for Type 1-PAF in $mathbb{E}{^{3}}$

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

Authors : Esin Şahin, Şerife Nevin Gürbüz

Pages : 1-14

View : 43 | Download : 14

Publication Date : 2025-06-30

Article Type : Research Paper

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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