Spatial Generalized Octonionic Curves
| dc.authorid | 0000-0002-9149-7811 | |
| dc.authorid | 0000-0003-1797-674X | |
| dc.authorid | 0000-0002-0256-1472 | |
| dc.contributor.author | Akbiyik, Mucahit | |
| dc.contributor.author | Alo, Jeta | |
| dc.contributor.author | Akbiyik, Seda Yamac | |
| dc.date.accessioned | 2026-01-31T15:09:04Z | |
| dc.date.available | 2026-01-31T15:09:04Z | |
| dc.date.issued | 2025 | |
| dc.department | İstanbul Beykent Üniversitesi | |
| dc.description.abstract | This study investigates curves in a 7-dimensional space, represented by spatial generalized octonion-valued functions of a single variable, where the general octonions include real, split, semi, split semi, quasi, split quasi, and para octonions. We begin by constructing a new frame, referred to as the G2-frame, for spatial generalized octonionic curves, and subsequently derive the corresponding derivative formulas. We also present the connection between the G2-frame and the standard orthonormal basis of spatial generalized octonions. Moreover, we verify that Frenet-Serret formulas hold for spatial generalized octonionic curves. We establish the G2-congruence of two spatial generalized octonionic curves and present the correspondence between the Frenet-Serret frame and the G2-frame. A key advantage of the G2-frame is that the associated frame equations involve lower-order derivatives. This method is both time-efficient and computationally efficient. To demonstrate the theory, we present an example of a unit-speed spatial generalized octonionic curve and compute its G2-frame and invariants using MATLAB. | |
| dc.identifier.doi | 10.3390/axioms14090665 | |
| dc.identifier.issn | 2075-1680 | |
| dc.identifier.issue | 9 | |
| dc.identifier.uri | https://doi.org./10.3390/axioms14090665 | |
| dc.identifier.uri | https://hdl.handle.net/20.500.12662/10812 | |
| dc.identifier.volume | 14 | |
| dc.identifier.wos | WOS:001579404500001 | |
| dc.identifier.wosquality | Q2 | |
| dc.indekslendigikaynak | Web of Science | |
| dc.language.iso | en | |
| dc.publisher | Mdpi | |
| dc.relation.ispartof | Axioms | |
| dc.relation.publicationcategory | Makale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı | |
| dc.rights | info:eu-repo/semantics/openAccess | |
| dc.snmz | KA_WoS_20260128 | |
| dc.subject | generalized octonions | |
| dc.subject | curvatures | |
| dc.subject | Frenet-Serret frame formulae | |
| dc.title | Spatial Generalized Octonionic Curves | |
| dc.type | Article |
