10 papers
Horocyclic evolutes, parallels and involutes of spacelike frontals in hyperbolic 2-space
Nozomi Nakatsuyama, Masatomo Takahashi, Anjie Zhou
The horocyclic evolutes of spacelike frontals in hyperbolic 2-space have already been defined. Using enveloid theorem, we now define the horocyclic parallel and involute of a space…
Evolutes and involutes of framed curves in Euclidean 3-space
Nozomi Nakatsuyama
We investigated the evolute of a space curve with singular points. As smooth curves with singular points, we apply the theory of framed curves. However, the involute corresponding…
Bertrand Legendre curves in the unit tangent bundle over Euclidean plane
Nozomi Nakatsuyama, Masatomo Takahashi
We investigate not only the associated curves of regular plane curves, but also those of Legendre curves. As associated curves, we consider Bertrand regular plane curves and Bertra…
Curvature equivalence for Legendre curves in the unit tangent bundle over Euclidean plane
Nozomi Nakatsuyama, Masatomo Takahashi, Minoru Yamamoto
The Legendre curve in the unit tangent bundle over Euclidean plane is a plane curve with a moving frame. We have the (Legendre) curvature of the Legendre curve, and the existence a…
Singularities of translation surfaces under the linearly dependent condition in Euclidean 3-space
Tomonori Fukunaga, Nozomi Nakatsuyama, Masatomo Takahashi
We investigated singular points of translation surfaces under the linearly independent condition. In this paper, as completion, we investigate singular points of translation surfac…
Bertrand framed surfaces in the Euclidean 3-space and its applications
Nozomi Nakatsuyama, Masatomo Takahashi
A framed surface is a smooth surface in the Euclidean space with a moving frame. By using the moving frame, we can define Bertrand framed surfaces as the same idea as Bertrand fram…