In the domain $ \Omega\subset E_{5} $ we consider a set of smooth lines such that through each point $X\in\Omega$ there passes exactly one line $\omega^{1}$ from the given set. The moving frame of the domain $\Omega$ is a Frenet frame \cite{Rashevsky} associated with the line $\omega^{1}$. The integral lines of the coordinate vector fields form a Frenet net \cite{Rashevsky}. We define the point $F_{1}^{5}$ on the tangent of the line $\omega^{1}$ in an invariant manner. As the point $X$ moves within the domain $\Omega$, the point $F_{1}^{5}$ traces out a new domain $\Omega_{1}^{5}\subset E_{5}$. This defines the partial mapping $f_{1}^{5}:\Omega \rightarrow \Omega_{1}^{5}$ such that $f_{1}^{5}(X)=F_{1}^{5}$. Similarly, we define another partial mapping $f_{5}^{4}:\Omega \rightarrow \Omega_{5}^{4}$ Next, we consider the composition of these two partial mappings, specifically the inverse mapping $(f_{1}^{5})^{-1}$ and $f_{5}^{4}$ given by: $f_{5}^{4}\circ (f_{1}^{5})^{-1} :\Omega_{1}^{5} \rightarrow \Omega_{5}^{4}$ such that $f_{5}^{4}\circ (f_{1}^{5})^{-1}(F_{1}^{5})=F_{5}^{4}$, where $(f_{1}^{5})^{-1}$ - is the inverse mapping $f_{1}^{5}$. Let the line $\gamma$, which belongs to the distribution $\Delta_{4}=(X,\overrightarrow{e}_{2},\overrightarrow{e}_{3},\overrightarrow{e}_{4},\overrightarrow{e}_{5})$ be a quasi-double line of the pair of distributions $(\Delta_{4},\Delta'_{4})$ in the partial mapping $f_{1}^{5}$ (where $\Delta'_{4}=f_{1}^{5}(\Delta_{4})$). We establish necessary and sufficient conditions for the line $f_{5}^{4}\circ (f_{1}^{5})^{-1}(\gamma)$ to be a quasi-double line of the pair $(\Delta_{4},\Delta'_{4})$ of distributions $\Delta_{4},\Delta'_{4}$in the partial mapping $f_{5}^{4}\circ (f_{1}^{5})^{-1}$.
| Mualliflar | Matieva , G., Papieva , T.M., Shamshieva , G.A. |
|---|---|
| Jurnal | O‘zbekiston matematika jurnali |
| Nashriyot | Ўзбекистон Республикаси ФА Математика институти |
| ISSN | 2010-7269 |
| Nashr sanasi | 2025-11-03 |
| Jild | 69 |
| Son | 4 |
| Betlar | 165-168 |
| Til | Ingliz |
| Ilmiy soha | Fizika-matematika |
| DOI | 10.29229/uzmj.2025-4-16 |
| Indeksga qo‘shilgan | 2026-08-26 |
DOI: 10.29229/uzmj.2025-4-16 · Maqolaning asl sahifasi
Euclidean space, Frenet frame, cyclic Frenet net, partial mapping, quasi-double line, distribution
| APA | Matieva , G., Papieva , T.M., & Shamshieva , G.A. (2025). About one composition of partial mapping of Euclidean space $E_{5}$. O‘zbekiston matematika jurnali, 69(4), 165-168. https://doi.org/10.29229/uzmj.2025-4-16 |
|---|---|
| GOST (OAK) | Matieva , G., Papieva , T.M., Shamshieva , G.A. About one composition of partial mapping of Euclidean space $E_{5}$ // O‘zbekiston matematika jurnali. – 2025. – T. 69, № 4. – P. 165-168. – DOI: 10.29229/uzmj.2025-4-16. |
| MLA | Matieva , G., Papieva , T.M., and Shamshieva , G.A. “About one composition of partial mapping of Euclidean space $E_{5}$.” O‘zbekiston matematika jurnali, 69(4), 165-168, 2025. https://doi.org/10.29229/uzmj.2025-4-16 |
| Chicago | Matieva , G., Papieva , T.M., and Shamshieva , G.A. “About one composition of partial mapping of Euclidean space $E_{5}$.” O‘zbekiston matematika jurnali, 69(4), 165-168 (2025). https://doi.org/10.29229/uzmj.2025-4-16 |
| Harvard | Matieva , G., Papieva , T.M., and Shamshieva , G.A (2025) ‘About one composition of partial mapping of Euclidean space $E_{5}$’, O‘zbekiston matematika jurnali, 69(4), 165-168. https://doi.org/10.29229/uzmj.2025-4-16 |
| BibTeX | @article{matievag2025,
title = {About one composition of partial mapping of Euclidean space $E_{5}$},
author = {Matieva , G. and Papieva , T.M. and Shamshieva , G.A.},
journal = {O‘zbekiston matematika jurnali},
year = {2025},
volume = {69},
number = {4},
pages = {165-168},
doi = {10.29229/uzmj.2025-4-16},
url = {https://doi.org/10.29229/uzmj.2025-4-16}
} |
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