#### Generalized osculating curves of type (n-3) in the n-dimensional Euclidean space

Yıl: 2022 Cilt: 71 Sayı: 1 Sayfa Aralığı: 212 - 225 Metin Dili: İngilizce İndeks Tarihi: 29-07-2022

Generalized osculating curves of type (n-3) in the n-dimensional Euclidean space

Öz:
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.
Anahtar Kelime: unit speed curve Osculating curve higher order linear differential equation curvatures

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık
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 APA Bektaş Ö, Bekiryazıcı Z (2022). Generalized osculating curves of type (n-3) in the n-dimensional Euclidean space. , 212 - 225. 10.31801/cfsuasmas.845845 Chicago Bektaş Özcan,Bekiryazıcı Zafer Generalized osculating curves of type (n-3) in the n-dimensional Euclidean space. (2022): 212 - 225. 10.31801/cfsuasmas.845845 MLA Bektaş Özcan,Bekiryazıcı Zafer Generalized osculating curves of type (n-3) in the n-dimensional Euclidean space. , 2022, ss.212 - 225. 10.31801/cfsuasmas.845845 AMA Bektaş Ö,Bekiryazıcı Z Generalized osculating curves of type (n-3) in the n-dimensional Euclidean space. . 2022; 212 - 225. 10.31801/cfsuasmas.845845 Vancouver Bektaş Ö,Bekiryazıcı Z Generalized osculating curves of type (n-3) in the n-dimensional Euclidean space. . 2022; 212 - 225. 10.31801/cfsuasmas.845845 IEEE Bektaş Ö,Bekiryazıcı Z "Generalized osculating curves of type (n-3) in the n-dimensional Euclidean space." , ss.212 - 225, 2022. 10.31801/cfsuasmas.845845 ISNAD Bektaş, Özcan - Bekiryazıcı, Zafer. "Generalized osculating curves of type (n-3) in the n-dimensional Euclidean space". (2022), 212-225. https://doi.org/10.31801/cfsuasmas.845845
 APA Bektaş Ö, Bekiryazıcı Z (2022). Generalized osculating curves of type (n-3) in the n-dimensional Euclidean space. Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics, 71(1), 212 - 225. 10.31801/cfsuasmas.845845 Chicago Bektaş Özcan,Bekiryazıcı Zafer Generalized osculating curves of type (n-3) in the n-dimensional Euclidean space. Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics 71, no.1 (2022): 212 - 225. 10.31801/cfsuasmas.845845 MLA Bektaş Özcan,Bekiryazıcı Zafer Generalized osculating curves of type (n-3) in the n-dimensional Euclidean space. Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics, vol.71, no.1, 2022, ss.212 - 225. 10.31801/cfsuasmas.845845 AMA Bektaş Ö,Bekiryazıcı Z Generalized osculating curves of type (n-3) in the n-dimensional Euclidean space. Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics. 2022; 71(1): 212 - 225. 10.31801/cfsuasmas.845845 Vancouver Bektaş Ö,Bekiryazıcı Z Generalized osculating curves of type (n-3) in the n-dimensional Euclidean space. Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics. 2022; 71(1): 212 - 225. 10.31801/cfsuasmas.845845 IEEE Bektaş Ö,Bekiryazıcı Z "Generalized osculating curves of type (n-3) in the n-dimensional Euclidean space." Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics, 71, ss.212 - 225, 2022. 10.31801/cfsuasmas.845845 ISNAD Bektaş, Özcan - Bekiryazıcı, Zafer. "Generalized osculating curves of type (n-3) in the n-dimensional Euclidean space". Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics 71/1 (2022), 212-225. https://doi.org/10.31801/cfsuasmas.845845