10 papers
Evolutes, involutes and parallels of Legendre curves in hyperbolic and de Sitter 2-spaces via rotational transformations
Nozomi Nakatsuyama, Masatomo Takahashi, Anjie Zhou
We develop a unified approach to constructing the moving frames of the evolute, involute and parallel of a Legendre curve via rotational transformations (rotation, boost and null r…
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…
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…
Bertrand lightcone framed curves in the Lorentz-Minkowski 3-space
Nozomi Nakatsuyama, Masatomo Takahashi
We consider mixed types of not only regular curves but also curves with singular points in the Lorentz-Minkowski 3-space. In order to consider mixed type of curves with singular po…
Singularities of helicoidal surfaces of frontals in the Euclidean space
N. Nakatsuyama, K. Saji, R. Shimada +1
We investigate helicoidal (screw) surfaces generated not only by regular curves but also by curves with singular points. For curves with singular points, it is useful to use fronta…
Bertrand types of regular curves and Bertrand framed curves in the Euclidean 3-space
Nozomi Nakatsuyama, Masatomo Takahashi
A Bertrand (respectively, Mannheim) curve is a space curve whose principal normal line is the same as the principal normal (respectively, bi-normal) line of another curve. By defin…
On vertices of frontals in the Euclidean plane
Nozomi Nakatsuyama, Masatomo Takahashi
We investigate vertices for plane curves with singular points. As plane curves with singular points, we consider Legendre curves (respectively, Legendre immersions) in the unit tan…