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.
Primary Language | English |
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Subjects | Mathematical Sciences |
Journal Section | Research Articles |
Authors | |
Publication Date | March 30, 2022 |
Submission Date | December 23, 2020 |
Acceptance Date | August 18, 2021 |
Published in Issue | Year 2022 Volume: 71 Issue: 1 |
Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.
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