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math.DG2025
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…
math.DG2025
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…