Quaternionic Similar Curves in 4-dimensional Euclidean Space

TL;DR

This paper introduces quaternionic similar curves in 4D Euclidean space, showing that families with vanishing curvatures are examples of such curves, expanding the understanding of quaternionic geometry in higher dimensions.

Contribution

It defines quaternionic similar curves in 4D Euclidean space and characterizes them via families with vanishing curvatures, a novel approach in quaternionic differential geometry.

Findings

Families of quaternionic curves with zero curvature are quaternionic similar curves

The paper establishes a new geometric relationship in 4D quaternionic space

Provides foundational concepts for further studies in quaternionic geometry

Abstract

In this paper, we introduce the quaternionic similar curves in 4-dimensional Euclidean space. We show that the families of quaternionic curves with vanishing curvatures form the families of quaternionic similar curves.