Null Hybrid Curves and Some Characterizations of Null Hybrid Bertrand Curves
| dc.contributor.author | Alo, Jeta | |
| dc.date.accessioned | 2026-01-31T15:04:30Z | |
| dc.date.available | 2026-01-31T15:04:30Z | |
| dc.date.issued | 2025 | |
| dc.department | İstanbul Beykent Üniversitesi | |
| dc.description.abstract | In this paper, we investigate null curves in (Formula presented.), the four-dimensional Minkowski space of index 2, utilizing the concept of hybrid numbers. Hybrid and spatial hybrid-valued functions of a single variable describe a curve in (Formula presented.). We first derive Frenet formulas for a null curve in (Formula presented.), the three-dimensional Minkowski space of index 2, by means of spatial hybrid numbers. Next, we apply the Frenet formulas for the associated null spatial hybrid curve corresponding to a null hybrid curve in order to derive the Frenet formulas for this curve in (Formula presented.). This approach is simpler and more efficient than the classical differential geometry methods and enables us to determine a null curve in (Formula presented.) corresponding to the null curve in (Formula presented.). Additionally, we provide an example of a null hybrid curve, demonstrate the construction of its Frenet frame, and calculate the curvatures of the curve. Finally, we introduce null hybrid Bertrand curves, and by using their symmetry properties, we provide some characterizations of these curves. © 2025 by the author. | |
| dc.identifier.doi | 10.3390/sym17020312 | |
| dc.identifier.issue | 2 | |
| dc.identifier.scopus | 2-s2.0-85219060088 | |
| dc.identifier.scopusquality | Q1 | |
| dc.identifier.uri | https://doi.org/10.3390/sym17020312 | |
| dc.identifier.uri | https://hdl.handle.net/20.500.12662/10571 | |
| dc.identifier.volume | 17 | |
| dc.indekslendigikaynak | Scopus | |
| dc.language.iso | en | |
| dc.publisher | Multidisciplinary Digital Publishing Institute (MDPI) | |
| dc.relation.ispartof | Symmetry | |
| dc.relation.publicationcategory | Makale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı | |
| dc.rights | info:eu-repo/semantics/openAccess | |
| dc.snmz | KA_Scopus_20260128 | |
| dc.subject | Bertrand curves | |
| dc.subject | Frenet equations | |
| dc.subject | hybrid numbers | |
| dc.subject | null Bertrand curves | |
| dc.subject | null curves | |
| dc.subject | null hybrid curves | |
| dc.title | Null Hybrid Curves and Some Characterizations of Null Hybrid Bertrand Curves | |
| dc.type | Article |
