Generalized normal ruled surface of a curve in the Euclidean 3-space

Generalized normal ruled surface of a curve in the Euclidean 3-space

In this study, we define the generalized normal ruled surface of a curve in the Euclidean 3-space E3. We study the geometry of such surfaces by calculating the Gaussian and mean curvatures to determine when the surface is flat or minimal (equivalently, helicoid). We examine the conditions for the cu...

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Main Authors: Kaya Onur, Önder Mehmet
Format: Article
Language:English
Published: Sciendo 2021-08-01
Series:Acta Universitatis Sapientiae: Mathematica
Subjects:
normal ruled surface
minimal surface
helix
slant ruled surface
53a05
53a25
Online Access:https://doi.org/10.2478/ausm-2021-0013
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spelling doaj-d8a03d51f45c4206aa327854d2a67f5b2021-09-22T06:13:22ZengSciendoActa Universitatis Sapientiae: Mathematica2066-77522021-08-0113121723810.2478/ausm-2021-0013Generalized normal ruled surface of a curve in the Euclidean 3-spaceKaya Onur0Önder Mehmet1Manisa Celal Bayar University, TurkeyIndependent ResearcherIn this study, we define the generalized normal ruled surface of a curve in the Euclidean 3-space E3. We study the geometry of such surfaces by calculating the Gaussian and mean curvatures to determine when the surface is flat or minimal (equivalently, helicoid). We examine the conditions for the curves lying on this surface to be asymptotic curves, geodesics or lines of curvature. Finally, we obtain the Frenet vectors of generalized normal ruled surface and get some relations with helices and slant ruled surfaces and we give some examples for the obtained results.https://doi.org/10.2478/ausm-2021-0013normal ruled surfaceminimal surfacehelixslant ruled surface53a0553a25
collection DOAJ
language English
format Article
sources DOAJ
author Kaya Onur
Önder Mehmet
spellingShingle Kaya Onur
Önder Mehmet
Generalized normal ruled surface of a curve in the Euclidean 3-space
Acta Universitatis Sapientiae: Mathematica
normal ruled surface
minimal surface
helix
slant ruled surface
53a05
53a25
author_facet Kaya Onur
Önder Mehmet
author_sort Kaya Onur
title Generalized normal ruled surface of a curve in the Euclidean 3-space
title_short Generalized normal ruled surface of a curve in the Euclidean 3-space
title_full Generalized normal ruled surface of a curve in the Euclidean 3-space
title_fullStr Generalized normal ruled surface of a curve in the Euclidean 3-space
title_full_unstemmed Generalized normal ruled surface of a curve in the Euclidean 3-space
title_sort generalized normal ruled surface of a curve in the euclidean 3-space
publisher Sciendo
series Acta Universitatis Sapientiae: Mathematica
issn 2066-7752
publishDate 2021-08-01
description In this study, we define the generalized normal ruled surface of a curve in the Euclidean 3-space E3. We study the geometry of such surfaces by calculating the Gaussian and mean curvatures to determine when the surface is flat or minimal (equivalently, helicoid). We examine the conditions for the curves lying on this surface to be asymptotic curves, geodesics or lines of curvature. Finally, we obtain the Frenet vectors of generalized normal ruled surface and get some relations with helices and slant ruled surfaces and we give some examples for the obtained results.
topic normal ruled surface
minimal surface
helix
slant ruled surface
53a05
53a25
url https://doi.org/10.2478/ausm-2021-0013
work_keys_str_mv AT kayaonur generalizednormalruledsurfaceofacurveintheeuclidean3space
AT ondermehmet generalizednormalruledsurfaceofacurveintheeuclidean3space
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