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arXiv · 2610.38111

New Explicit Examples of Mannheim Pairs in $\mathbb{R}^3$

José Alan·Renato Teixeira·Thiago Mendonça
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Abstract

In this paper, we construct new explicit parametrizations of Mannheim pairs in Euclidean 3-space. Unlike the known examples in the literature, which are essentially slant helices or general helices, the curve presented here is neither a helix nor a slant helix. We provide the full Frenet apparatus, the explicit Cartesian coordinates expressed in terms of elementary functions, and the corresponding Mannheim partner curve. The construction is based on a specific choice of the angular function that governs the curve's tangent indicatrix, leading to integrable expressions.

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José Alan, Renato Teixeira, Thiago Mendonça. 2026-10-28. New Explicit Examples of Mannheim Pairs in $\mathbb{R}^3$. https://arxiv.org/abs/2610.38111

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