Browsing by Subject "Helix surface"

Now showing 1 - 3 of 3
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    A property that characterizes the Enneper surface and helix surfaces
    (Springer, 2024-06-29) Lucas Saorín, Pascual; Otega Yagües, José Antonio; Matemáticas
    The main goal of this paper is to show that helix surfaces and the Enneper surface are theonly surfaces in the 3-dimensional Euclidean space R3 whose isogonal lines are generalizedhelices and pseudo-geodesic lines.
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    Concircular helices and concircular surfaces in Euclidean 3-space R3
    (Universidad de Hacettepe, 2023) Lucas Saorín, Pascual; Ortega Yagües, José Antonio; Matemáticas
    In this paper we characterize concircular helices in R3 by means of a differential equation involving their curvature and torsion. We find a full description of concircular surfaces in R3 as a special family of ruled surfaces, and we show that M ⊂ R3 is a proper concircular surface if and only if either M is parallel to a conical surface or M is the normal surface to a spherical curve. Finally, we characterize the concircular helices as geodesics of concircular surfaces.
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    Concircular hypersurfaces and concircular helices inspace forms
    (Springer, 2023-08-23) Lucas Saorín, Pascual; Ortega Yagües, José Antonio; Matemáticas
    In this paper, we find a full description of concircular hypersurfaces in spaceforms as a special family of ruled hypersurfaces. We also characterize concircularhelices in 3-dimensional space forms by means of a differential equation involving theconcircular factor and their curvature and torsion, and we show that the concircularhelices are precisely the geodesics of the concircular surfaces.