Framed Natural Mates of Framed Curves in Euclidean 3-Space

Yanlin Li () and Mahmut Mak
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Yanlin Li: School of Mathematics, Hangzhou Normal University, Hangzhou 311121, China
Mahmut Mak: Department of Mathematics, Kırşehir Ahi Evran University, Kırşehir 40100, Turkey

Mathematics, 2023, vol. 11, issue 16, 1-14

Abstract: In this study, we consider framed curves as regular or singular space curves with an adapted frame in Euclidean 3-space. We define framed natural mates of a framed curve that are tangent to the generalized principal normal of the framed curve. Subsequently, we present the relationships between a framed curve and its framed natural mates. In particular, we establish some necessary and sufficient conditions for the framed natural mates of specific framed curves, such as framed spherical curves, framed helices, framed slant helices, and framed rectifying curves. Finally, we support the concept with some examples.

Keywords: framed curve; spherical curve; helix; slant helix; rectifying curve (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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