Nozomi Nakatsuyama
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Nozomi Nakatsuyama has a total of 4 co-authors. Here are the top co-authors by number of shared publications:
- Masatomo Takahashi
Muroran Institute of Technology, Muroran, Japan
4 shared publications - Kentaro Saji
Kobe University, Kobe, Japan
1 shared publication - Runa Shimada
Department of Mathematics, Graduate School of Science, Kobe University, Nada, Kobe, Japan
1 shared publication Tomonori Fukunaga
1 shared publication
Latest Publications
- Open Access
Singularities of translation surfaces under the linearly dependent condition in Euclidean 3-space
We investigated singular points of translation surfaces under the linearly independent condition. In this paper, as completion, we investigate singular points of translation surfaces under the linearly dependent condition, using the theories of generalised framed surfaces and framed surfaces. We introduce the notion of translation generalised framed surfaces and investigate types of singular points that appear on translation generalised framed base surfaces.
Open AccessSingularities of translation surfaces under the linearly dependent condition in Euclidean 3-space
We investigated singular points of translation surfaces under the linearly independent condition. In this paper, as completion, we investigate singular points of translation surfaces under the linearly dependent condition, using the theories of generalised framed surfaces and framed surfaces. We introduce the notion of translation generalised framed surfaces and investigate types of singular points that appear on translation generalised framed base surfaces.
- 31 October 2025
- Published by Springer Nature in Research in the Mathematical Sciences
- Vol. 12 (4) , 1-24
Bertrand framed surfaces in the Euclidean 3-space and its applications
- 31 October 2025
- Published by Springer Nature in Research in the Mathematical Sciences
- Vol. 12 (4) , 1-24
Bertrand framed surfaces in the Euclidean 3-space and its applications
- 24 October 2025
- Published by Springer Nature in Indian Journal of Pure and Applied Mathematics
- p. 1-16
Singularities of helicoidal surfaces of frontals in the Euclidean space
- 24 October 2025
- Published by Springer Nature in Indian Journal of Pure and Applied Mathematics
- p. 1-16
Singularities of helicoidal surfaces of frontals in the Euclidean space
- Open Access
Bertrand framed surfaces in the Euclidean 3-space and its applications
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 framed curves. Then we find the caustics and involutes as Bertrand framed surfaces. As applications, we can directly define the caustics and involutes of framed surfaces, and give conditions that the caustics and involutes are inverse operations of framed surfaces like as those of Legendre curves. Moreover, a framed surface is one of the Bertrand framed surfaces if and only if another caustic of the involute exists, under conditions. Furthermore, we find a new such operation, the so-called tangential direction framed surfaces.
Open AccessBertrand framed surfaces in the Euclidean 3-space and its applications
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 framed curves. Then we find the caustics and involutes as Bertrand framed surfaces. As applications, we can directly define the caustics and involutes of framed surfaces, and give conditions that the caustics and involutes are inverse operations of framed surfaces like as those of Legendre curves. Moreover, a framed surface is one of the Bertrand framed surfaces if and only if another caustic of the involute exists, under conditions. Furthermore, we find a new such operation, the so-called tangential direction framed surfaces.