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

Bekiryazıcı, Zafer; Bektaş, Özcan

doi:10.31801/cfsuasmas.845845

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

Özcan BEKTAŞ, (Recep Tayyip Erdoğan Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü, Rize, Türkiye)

Zafer BEKİRYAZICI (Recep Tayyip Erdoğan Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü, Rize, Türkiye)

Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics

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Yıl: 2022 Cilt: 71 Sayı: 1 Sayfa Aralığı: 212 - 225 Metin Dili: İngilizce DOI: 10.31801/cfsuasmas.845845 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