Alternative planes and the curves on them
Résumé
In this study, the planes formed by Frenet elements are defined with a U vector chosen different from T, N and B, which are the elements of the Frenet frame, and the curves on these planes are also characterized. As it is known, the planes formed by Frenet elements between themselves have been defined and investigated many times. In this present article, the plane formed by an arbitrary chosen vector U with T, N and B is defined and the curves
lying in this plane are characterized
Téléchargements
Références
At, A. and Onder, M., Some characterizations of space-like rectifying curves in the Minkowski space-time. Glob. J. Sci. Front Res. Math. Decision Sci., 12(1), 57-64, (2012).
Cambie, S., Goemans, W. and Van Den Bussche, I., Rectifying curves in n-dimensional Euclidean space. Turk. J. Math., 40, 210-223, (2016).
Chen, B. Y., When does the position vector of a space curve always lie in its rectifying plane. The American Mathematical Monthly, 110, 147-152, (2003).
Chen, B. Y. and Dillen, F., Rectifying curves as centrodes and extremal curves. Bulletin of the Institute of Mathematics Academia Sinica, 33(2), 77-90, (2005).
Ilarslan, K., Nesovic, E. and Petrovic-Torgasev, M., Some characterizations of rectifying curves in the Minkowski 3- space. Novi Sad Journal of Mathematic, 33(2), 23-32, (2003).
Ilarslan, K., Spacelike normal curves in Minkowski space E3 1 . Turk. J. Math., 29, 53-63, (2005).
Ilarslan, K. and Nesovic, E., Some characterizations of osculating curves in the Euclidean spaces. Demonstratio Mathematica, 41(4), 931-939, (2008).
Kulahcı, M.A., Bektas, M. and Bilici, A., On Classifications of Normal and Osculating Curves in 3-dimensional Sasakian Space. Mathematical Sciences and Applications E-Notes, 7(1), 120-127, (2019).
Oztekin, H. and Ogrenmis, A. O., Normal and rectifying curves in Pseudo-Galilean space G3 1 and their characterizations. J. Math. Comput. Sci., 2 , 91-100, (2012).
Struik, D. J., Lectures on Classical Diferential Geometry. Dover Publications, 1988.
Copyright (c) 2024 Boletim da Sociedade Paranaense de Matemática
Ce travail est disponible sous la licence Creative Commons Attribution 4.0 International .
When the manuscript is accepted for publication, the authors agree automatically to transfer the copyright to the (SPM).
The journal utilize the Creative Common Attribution (CC-BY 4.0).
