Quaternionic Salkowski Curves and Quaternionic Similar Curves

TL;DR

This paper introduces and characterizes quaternionic Salkowski, anti-Salkowski, and similar curves in Euclidean spaces, exploring their relationships with special quaternionic curves like slant helices.

Contribution

It provides new definitions and characterizations of quaternionic curves and their relationships with known special curves in Euclidean spaces.

Findings

Defined quaternionic Salkowski and anti-Salkowski curves.

Established relationships with quaternionic slant helices.

Characterized quaternionic similar curves in E^3 and E^4.

Abstract

In this paper, we give the definitions and characterizations of quaternionic Salkowski, quaternionic anti-Salkowski and quaternionic similar curves in the Euclidean spaces E^3 and E^4. We obtain relationships between these curves and some special quaternionic curves such as quaternionic slant helices and quaternionic B2-slant helices.