On split-octonionic curves
Küçük Resim Yok
Tarih
2024
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Oxford Univ Press
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
In this paper, we first define the vector product in Minkowski space $\mathbb{R}_{4}<^>{7}$ , which is identified with the space of spatial split-octonions. Next, we derive the $G_{2}-$ frame formulae for a seven dimensional Minkowski curve by using the spatial split-octonions and the vector product. We show that Frenet-Serret formulas are satisfied for a spatial split octonionic curve. We obtain the congruence of two spatial split octonionic curves and give relationship between the $G_{2}-$ frame and Frenet-Serret frame. Furthermore, we present the Frenet-Serret frame with split octonions in $\mathbb{R}_{4}<^>{8}$ . Finally, we give illustrative examples with Matlab codes.
Açıklama
Anahtar Kelimeler
53A35, 11R52, 14H50
Kaynak
Logic Journal of the Igpl
WoS Q Değeri
Q2
Scopus Q Değeri
Q1
