4 papers · 1 filter
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…