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

Kaixin Yao; Kaixin Yao

doi:10.3934/math.2026763

AIMS Mathematics

2026, Volume 11, Issue 6: 18772-18786. doi: 10.3934/math.2026763

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Research article

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

Kaixin Yao ^,

School of Science, Yanshan University, Qinhuangdao 066004, China

Received: 03 April 2026 Revised: 04 June 2026 Accepted: 16 June 2026 Published: 25 June 2026
MSC : 15A63, 53A35, 57R45

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.
- non-parabolic spatial hybrid framed curves,
- evolutes,
- involutes,
- pedal curves,
- contrapedal curves
Citation: Kaixin Yao. Non-parabolic spatial hybrid framed curves and their applications in the spatial hybrid number space[J]. AIMS Mathematics, 2026, 11(6): 18772-18786. doi: 10.3934/math.2026763

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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.

References

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