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arXiv · 2512.01347

Singularities of translation surfaces under the linearly dependent condition in Euclidean 3-space

Tomonori Fukunaga·Nozomi Nakatsuyama·Masatomo Takahashi
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Abstract

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.

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BibTeXRIS

Tomonori Fukunaga, Nozomi Nakatsuyama, Masatomo Takahashi. 2025-12-01. Singularities of translation surfaces under the linearly dependent condition in Euclidean 3-space. https://arxiv.org/abs/2512.01347

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