4 papers · 1 filter
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…