Generalized quaternionic involute-evolute curves in the Euclidean four-space E4期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Generalized quaternionic involute-evolute curves in the Euclidean four-space E4

Authors:	Muhammad Hanif Mehmet Önder

Affiliation:	1. School of Mathematical Sciences, Dalian University of Technology, Dalian, 116024 China;2. Independent Researcher, Delibekirli Village, Tepe Street, No. 63, Kırıkhan, Hatay, Turkey

Abstract:	In this paper, a new type of quaternionic partner curves is defined as generalized quaternionic involute-evolute curves or $(0, 2)$ -quaternionic involute– $(1, 3)$ -quaternionic evolute curves in the four-dimensional Euclidean space. The relations between the Frenet frames and curvatures of the quaternionic involute-evolute curve couple are introduced. Moreover, the necessary and sufficient conditions for a quaternionic curve to have a generalized involute are obtained.

Keywords:	generalized involute-evolute curves quaternionic curve quaternion algebra