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arXiv · 2608.26823

Evolutes, involutes and parallels of Legendre curves in hyperbolic and de Sitter 2-spaces via rotational transformations

Nozomi Nakatsuyama·Masatomo Takahashi·Anjie Zhou
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Abstract

We develop a unified approach to constructing the moving frames of the evolute, involute and parallel of a Legendre curve via rotational transformations (rotation, boost and null rotation). The definitions of the evolute, involute and parallel of a Legendre curve in hyperbolic and de Sitter 2-spaces are systematically presented. Furthermore, the connections and dualities among these curves are discussed.

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Nozomi Nakatsuyama, Masatomo Takahashi, Anjie Zhou. 2026-08-27. Evolutes, involutes and parallels of Legendre curves in hyperbolic and de Sitter 2-spaces via rotational transformations. https://arxiv.org/abs/2608.26823

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