1 citations · 1 across the 5 of their papers we have counts for
7 papers
Envelopes created by curve families in the Lorentz-Minkowski plane
Masatomo Takahashi, Yongqiao Wang
Classical definitions of envelopes are vague for singular curves in the Lorentz-Minkowski plane. To study envelopes of such curves, we introduce a family of smooth curves that may…
Envelopes created by sphere families in Euclidean 3-space
Takashi Nishimura, Masatomo Takahashi, Yongqiao Wang
In this paper, on envelopes created by sphere families in Euclidean 3-space, all four basic problems (existence problem, representation problem, problem on the number of envelopes,…
Inverse curvature flow of closed Legendre curves
Takashi Kagaya, Masatomo Takahashi
In this paper, we deal with an inverse curvature flow of -convex Legendre curves. Since the Legendre curve is a natural generalization of regular curve, the flow is a general…
Bertrand and Mannheim curves of framed curves in the 4-dimensional Euclidean space
Shun'ichi Honda, Masatomo Takahashi, Haiou Yu
A Bertrand curve in the 4-dimensional Euclidean space is a space curve whose first normal line is the same as the first normal line of another curve. On the other hand, a Mannheim…
Circular evolutes and involutes of framed curves in the Euclidean space
Shun'ichi Honda, Masatomo Takahashi
We introduce circular evolutes and involutes of framed curves in the Euclidean space. Circular evolutes of framed curves stem from the curvature circles of Bishop directions and si…
Geometric equivalence among smooth map germs
Shyuichi Izumiya, Masatomo Takahashi, Hiroshi Teramoto
We consider equivalence relations among smooth map germs with respect to geometry of G-structures on the target space germ. These equivalence relations are natural generalization o…