TY  - JOUR
TI  - Generalized osculating curves of type (n-3) in the n-dimensional Euclidean space
AB  - In this paper, we give a generalization of the osculating curves to the $n$-dimensional Euclidean space. Based on the definition of an osculating curve in the 3 and 4 dimensional Euclidean spaces, a new type of osculating curve has been defined such that the curve is independent of the (n−3)(n−3)th binormal vector in the n-dimensional Euclidean space, which has been called ”a generalized osculating curve of type (n−3)(n−3)”. We find the relationship between the curvatures for any unit speed curve to be congruent to this osculating curve in EnEn. In particular, we characterize the osculating curves in EnEn in terms of their curvature functions. Finally, we show that the ratio of the (n−1)(n−1)th and (n−2)(n−2)th curvatures of the osculating curve is the solution of an (n−2)(n−2)th order linear nonhomogeneous differential equation.
AU  - Bekiryazıcı, Zafer
AU  - Bektaş, Özcan
DO  - 10.31801/cfsuasmas.845845
PY  - 2022
JO  - Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics
VL  - 71
IS  - 1
SN  - 1303-5991
SP  - 212
EP  - 225
DB  - TRDizin
UR  - http://search/yayin/detay/511703
ER  -