Non-parabolic Spatial Hybrid Framed Curves and Their Applications in the Spatial Hybrid Number Space

TL;DR

This paper introduces a new class of spatial hybrid framed curves in the hybrid number space, explores their properties, and discusses their geometric applications such as evolutes and involutes.

Contribution

It defines non-parabolic spatial hybrid framed curves, proves their existence and uniqueness, and extends classical geometric concepts to this new framework.

Findings

Existence and uniqueness of non-parabolic spatial hybrid framed curves.

Definitions and relations of evolutes, involutes, pedal, and contrapedal curves in this context.

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. As applications, we define evolutes, involutes, pedal and contrapedal curves of non-parabolic spatial hybrid framed curves and discuss their relations.