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Research Article | Open Access

Non-parabolic spatial hybrid framed curves and their applications in the spatial hybrid number space

School of Science, Yanshan University, Qinhuangdao 066004, China
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Abstract

In this paper, we define non-parabolic spatial hybrid framed curves in the spatial hybrid number space, which may have singularities, and prove the existence and uniqueness theorem for non-parabolic spatial hybrid framed curves. We construct the Frenet type frame by linear combination of vectors in the original moving frame. As applications, we define evolutes, involutes, pedal and contrapedal curves of non-parabolic spatial hybrid framed curves and discuss their relations.

Keywords

non-parabolic spatial hybrid framed curvesevolutesinvolutespedal curvescontrapedal curves
CLC number: 15A63, 53A35, 57R45

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AIMS Mathematics
Volume 11 Issue 6,
June 2026
Pages 18772-18786
DOI: 10.3934/math.2026763

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Cite this article:
Yao K. Non-parabolic spatial hybrid framed curves and their applications in the spatial hybrid number space. AIMS Mathematics, 2026, 11(6): 18772-18786. https://doi.org/10.3934/math.2026763

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Received: 03 April 2026
Revised: 04 June 2026
Accepted: 16 June 2026
Published: 15 June 2026
©2026 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)