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- Title
On Special Kinds of Involute and Evolute Curves in 4-Dimensional Minkowski Space.
- Authors
Hanif, Muhammad; Hou, Zhong Hua; Nisar, Kottakkaran Sooppy
- Abstract
Recently, extensive research has been done on evolute curves in Minkowski space-time. However, the special characteristics of curves demand advanced level observations that are lacking in existing well-known literature. In this study, a special kind of generalized evolute and involute curve is considered in four-dimensional Minkowski space. We consider (1,3)-evolute curves with respect to the casual characteristics of the (1,3)-normal plane that are spanned by the principal normal and the second binormal of the vector fields and the (0,2)-evolute curve that is spanned by the tangent and first binormal of the given curve. We restrict our investigation of (1,3)-evolute curves to the (1,3)-normal plane in four-dimensional Minkowski space. This research contribution obtains a necessary and sufficient condition for the curve possessing the generalized evolute as well as the involute curve. Furthermore, the Cartan null curve is also discussed in detail.
- Subjects
MINKOWSKI geometry; MINKOWSKI space; VECTOR fields; VECTOR analysis; PHYSICS literature
- Publication
Symmetry (20738994), 2018, Vol 10, Issue 8, p317
- ISSN
2073-8994
- Publication type
Article
- DOI
10.3390/sym10080317