Abstract
In this paper, the spherical indicatrix curves drawn by quaternionic frenet vectors are computed. Also the quaternionic geodesic curvatures of the spherical indicatrix curves to E3 and S2 are found. Mathematics Subject Classification: 11R52, 53A04
Highlights
Quaternions were discovered, for the first time in 1843, by the Irish mathematician Sir William R
In 1987, Bharathi and Nagaraj defined the quaternionic curves in E3 and E4, they studied the differential geometry of space curves and introduced Frenet frames and formulae by using quaternions [4]
Senyurt and Calıskan have founded the Darboux vector of the spatial quaternionic curve according to the Frenet frame
Summary
Quaternions were discovered, for the first time in 1843, by the Irish mathematician Sir William R. They have given the Serret-Frenet formulae and they have defined quaternionic inclined curves and harmonic curvatures for the quaternionic curves in the semi-Euclidean space. Senyurt and Calıskan have founded the Darboux vector of the spatial quaternionic curve according to the Frenet frame. They calculated the curvature and torsion of the spatial quaternionic Smarandache curve formed by the unit Darboux vector with the normal vector, [7].
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