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SPINOR REPRESENTATIONS OF PAFORS IN E3
(Editura Bibliotheca-Bibliotheca Publ House, 2024) Isbilir, Zehra; Ozen, Kahraman Esen; Guner, Mehmet
In this paper, we introduce the spinor representations of PAFORS for the trajectories endowed with PAFORS on regular surfaces of Euclidean 3-space E-3. We find the spinor equations of PAFORS vectors. Moreover, we obtain the relations between spinor representations of PAFORS and Darboux frame. Then, we give some geometric interpretations and results concerned with this relationship.
Spinor Representations of Positional Adapted Frame in the Euclidean 3-Space
(Int Electronic Journal Geometry, 2023) Isbilir, Zehra; Ozen, Kahraman Esen; Guner, Mehmet
The main goal of this paper is to study together the spinors, which have a major place in several disciplines from mathematics to physics, and Positional Adapted Frame (PAF) which is a new frame that attracts the attention of many researchers. In accordance with this purpose, we introduce the spinor representations for the trajectories endowed with PAF in the Euclidean 3-space E3, and construct the spinor equations of PAF vectors. Then, we find the relations between spinor representations of PAF and Serret-Frenet frame. Also we give some results and present some geometric interpretations with respect to this relationship. Moreover, we present an illustrative numerical example in order to support the given theorems and results.