In this paper, a method for determination of developable spherical orthotomic ruled surfaces is given by using dual vector calculus. We show that dual vectorial expression of a developable spherical orthotomic ruled surface can be obtained from coordinates and the first derivatives of the base curve. The paper concludes with an example related to this method.

In this paper, we construct a helicoidal surface of type I ⁺ with prescribed weighted mean curvature and Gaussian curvature in the Minkowski 3 − space ℝ 1 3 ${\Bbb R}_1^3$ with a positive density function. We get a result for minimal case. Also, we give examples of a helicoidal surface with weighted mean curvature and Gaussian curvature.

In this paper, we introduce the adapted frame of framed curves and we give the relations between the adapted frame and Frenet type frame of the framed curve in four-dimensional Euclidean space. Moreover, we define the framed normal curves in four-dimensional Euclidean space. We obtain some characterizations of framed normal curves in terms of their framed curvature functions. Furthermore, we give the necessary and sufficient condition for a framed curve to be a framed normal curve.