Characterizing the developable surfaces with curves whose position vectors Lie in the planes spanned by Darboux frame

DOI10.1007/s13226-022-00267-0zbMath1517.53006OpenAlexW4281687724WikidataQ114220135 ScholiaQ114220135MaRDI QIDQ6107486

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Publication date: 3 July 2023

Published in: Indian Journal of Pure \& Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s13226-022-00267-0

zbMATH Keywords

developable surfaceDarboux frameconical surfaceosculating Darboux curverectifying Darboux curve

Mathematics Subject Classification ID

Global submanifolds (53C40) Surfaces in Euclidean and related spaces (53A05) Curves in Euclidean and related spaces (53A04)

Cites Work

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• Spherical Darboux images of curves on surfaces
• Generic properties of helices and Bertrand curves
• Special curves and ruled surfaces
• Curves always Lie in the plane spanned by Darboux frame
• Curves on a smooth surface with position vectors Lie in the tangent plane
• Flat approximations of surfaces along curves
• Normal developable surfaces of surfaces along curves
• When Does the Position Vector of a Space Curve Always Lie in Its Rectifying Plane?
• On rectifying curves in Euclidean 3-space
• Rectifying curves and geodesics on a cone in the Euclidean 3-space
• Flat surfaces along cuspidal edges

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