• Kyungpook Mathematical Journal
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• v.58 no.2
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• pp.377-388
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• 2018

In this paper, we define new quaternionic associated curves called quaternionic principal-direction curves and quaternionic principal-donor curves. We give some properties and relationships between Frenet vectors and curvatures of these curves. For spatial quaternionic curves, we give characterizations for quaternionic helices and quaternionic slant helices by means of their associated curves.

• Honam Mathematical Journal
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• v.46 no.2
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• pp.209-223
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• 2024

In this paper, we investigate the spatial quaternionic expressions of the ruled surfaces whose base curves are formed by the Smarandache curve. Moreover, we formulate the striction curves and dralls of these surfaces. If the quaternionic Smarandache ruled surfaces are closed, the pitches and angle of pitches are interpreted. Finally, we calculate the integral invariants of these surfaces using quaternionic formulas.

• Honam Mathematical Journal
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• v.36 no.1
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• pp.67-83
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• 2014

The notion of rectifying curve in the Euclidean space is introduced by Chen as a curve whose position vector always lies in its rectifying plane spanned by the tangent and the binormal vector field t and $n_2$ of the curve, [1]. In this study, we have obtained some characterizations of semi-real spatial quaternionic rectifying curves in $\mathbb{R}^3_1$. Moreover, by the aid of these characterizations, we have investigated semi real quaternionic rectifying curves in semi-quaternionic space $\mathbb{Q}_v$.

• Journal of the Korean Mathematical Society
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• v.35 no.4
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• pp.855-867
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• 1998

In the present paper, we introduce the notions of quaternionically planar curves and quaternionically projective transformations to the case of almost quaternionic manifold with symmetric affine connection. Also, we obtain an invariant tensor field under the quaternionically projective transformation, and show that a quaternionic Kahlerian manifold with such a vanishing tensor field is of constant Q-sectional curvature.