- Communications Faculty of Sciences University Ankara Series A1 Mathematics and Statistics
- Vol: 71 Issue: 1
- Generalized osculating curves of type (n-3) in the n-dimensional Euclidean space
Generalized osculating curves of type (n-3) in the n-dimensional Euclidean space
Authors : Özcan Bektaş, Zafer Bekiryazici
Pages : 212-225
Doi:10.31801/cfsuasmas.845845
View : 15 | Download : 2
Publication Date : 2022-03-30
Article Type : Research
Abstract :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 E n En . In particular, we characterize the osculating curves in E n En 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.Keywords : Osculating curve, curvatures, unit speed curve, higher order linear differential equation