Characterizations of Framed Curves in Four-Dimensional Euclidean Space
Abstract
Framed curves in Euclidean space are used to investigate singular curves and are important
for singularity theory. In this study, framed curves in four-dimensional Euclidean space are
introduced and new results are obtained. The relation of framed curves with Frenet curves
in four-dimensional Euclidean space is given and Bishop-type frame of framed curves is
introduced with the help of Euler angles. In addition, by using Bishop-type framed curves in
four-dimensional Euclidean space, framed rectifying curves, framed osculating curves and
framed normal curves are introduced. Also, some characterizations depending on framed
curvatures are obtained.
Keywords
Euler angles, Bishop-type framed curves, Framed curves in R4
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