DARBOUX-FRAMED BCV-LEGENDRE CURVE AND ASSOCIATED GEOMETRY
Özet
In this study, the components of the Darboux frame associated with a Legendre curve lying on a surface in the BCV-Sasakian
space are derived for the first time. The geometric invariants of the
curve, namely its normal curvature, geodesic curvature, and geodesic torsion, are explicitly computed. A canal surface is then constructed around
the Darboux-framed BCV-Legendre curve, leading to the formulation of
Darboux-framed BCV-Legendre tubes. The intrinsic and extrinsic geometry of these tubular surfaces is investigated by calculating their Gaussian
and mean curvatures. Moreover, the relationships between the parameter curves and geodesics, asymptotic curves, and curvature lines on the
Darboux-framed BCV-Legendre tubes are analyzed in detail. All of these
results are obtained for the first time in the context of BCV-Sasakian geometry, thus providing an original and significant contribution to the
differential geometry of contact manifolds
Atıf için künye
Ağirman Aydin, T., Ağırman, E., & Kocayiğit, H. (2025). DARBOUX-FRAMED BCV-LEGENDRE CURVE AND ASSOCIATED GEOMETRY. Honam Mathematical Journal, 47(4), 498–512. https://doi.org/10.5831/hmj.2025.47.4.498
BibTeX
@article{agirmanaydin2025-105681,
author = {Ağirman Aydin, Tuba and Ağırman, Ensar and Kocayiğit, Hüseyin},
title = {DARBOUX-FRAMED BCV-LEGENDRE CURVE AND ASSOCIATED GEOMETRY},
journal = {Honam Mathematical Journal},
year = {2025},
volume = {47},
number = {4},
pages = {498--512},
issn = {2288-6176},
doi = {10.5831/hmj.2025.47.4.498},
url = {https://akademik.atauni.edu.tr/yayinlar/105681-darboux-framed-bcv-legendre-curve-and-associated-geometry}
}