The Dual Expression of Parallel Equidistant Ruled Surfaces in Euclidean 3-Space
Erişim
info:eu-repo/semantics/openAccessTarih
2022Erişim
info:eu-repo/semantics/openAccessÜst veri
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Export citation file: BibTeX | EndNote | RIS MDPI and ACS Style Gür Mazlum, S.; Şenyurt, S.; Grilli, L. The Dual Expression of Parallel Equidistant Ruled Surfaces in Euclidean 3-Space. Symmetry 2022, 14, 1062. https://doi.org/10.3390/sym14051062 AMA Style Gür Mazlum S, Şenyurt S, Grilli L. The Dual Expression of Parallel Equidistant Ruled Surfaces in Euclidean 3-Space. Symmetry. 2022; 14(5):1062. https://doi.org/10.3390/sym14051062 Chicago/Turabian Style Gür Mazlum, Sümeyye, Süleyman Şenyurt, and Luca Grilli. 2022. "The Dual Expression of Parallel Equidistant Ruled Surfaces in Euclidean 3-Space" Symmetry 14, no. 5: 1062. https://doi.org/10.3390/sym14051062Özet
In this study, we examine the dual expression of Valeontis' concept of parallel p-equidistant ruled surfaces well known in Euclidean 3-space, according to the Study mapping. Furthermore, we show that the dual part of the dual angle on the unit dual sphere corresponds to the p-distance. We call these ruled surfaces we obtained "dual parallel equidistant ruled surfaces" and we briefly denote them with "DPERS". Furthermore, we find the Blaschke vectors, the Blaschke invariants and the striction curves of these DPERS and we give the relationships between these elements. Moreover, we show the relationships between the Darboux screws, the instantaneous screw axes, the instantaneous dual Pfaff vectors and dual Steiner rotation vectors of these surfaces. Finally, we give an example, which we reinforce this article, and we explain all of these features with the figures on the example. Furthermore, we see that the corresponding dual curves on the dual unit sphere to these DPERS are such that one of them is symmetric with respect to the imaginary symmetry axis of the other.
