Framed Natural Mates of Framed Curves in Euclidean 3-Space
Yanlin Li, Mahmut Mak
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.
Topics & Concepts
Natural (archaeology)Space (punctuation)TangentMathematicsPrincipal (computer security)Euclidean geometryGeometryMathematical analysisPure mathematicsComputer scienceGeologyOperating systemPaleontologyAdvanced Differential Geometry ResearchGeometric Analysis and Curvature FlowsPoint processes and geometric inequalities