Öz
Kaynakça
- Honda, S., Takahashi, M.: Framed curves in the Euclidean space, Advances in Geometry, 16(3), 265-276 (2016)
- Wang, Y., Pei, D., Gao, R., Generic properties of framed rectifying curves, Mathematics,7, 37 (2019)
- Dogan Yazıcı, B., Özkaldı Karakuş, S., Tosun, M., Framed normal curves in Euclidean space, Tbilisi Mathematical Journal, 27-37 (2019)
- Honda, S., Takahashi, M., Evolutes and focal surfaces of framed immersions in the Euclidean space, Proceedings of the Royal Society of Edinburgh Sect. A., 150(1), 497-516 (2019)
- Fukunaga, T., Takahashi, M., Existence conditions of framed curves for smooth curves, Journal of Geometry, 108, 763-774 (2017)
- Honda, S., Rectifying developable surfaces of framed base curves and framed helices, Advanced Studies in Pure Mathematics, 78, 273-292 (2018)
- Deshmukh, S., Chen B.Y., Turki, N.B.: A differential equations for Frenet curves in Euclidean 3-space and its applications. Rom. J. Math. Comput. Sci, 8(1), 1-6 (2018)
- Chen, B.Y., When does the position vector of a space curve always lie in its rectifying plane?, Amer Math Monthly, 110, 147-152 (2003)
- Chen, B.Y., Dillen, F., Rectifying curves as centrodes and extremal curves. Bull Inst Math Academia Sinica, 33, 77-90 (2005)
- Deshmukh, S., Chen B.Y., Alshammari S.H.: On rectifying curves in Euclidean 3-space, Turk J Math, 42(2), 609-620 (2018)
Öz
Characterization is very important for non-regular curves in differential geometry. Recently, the concept of framed curve has been proposed to examine a non-regular curve. Framed curves are defined as smooth curves with a moving frame that can have singular points. In this paper, the differential equation is obtained by using distance squared functions for framed curves with for each $p,q\neq 0$ framed curvatures in Euclidean space. Next, we give the relationships between this differential equation and some special curves. Moreover we intoduce a new equation of framed helices with the help of this differential equation. Moreover, these are support by some examples and figures.
Anahtar Kelimeler
framed curves framed spherical curves framed helices framed rectifying curves singular points
Kaynakça
- Honda, S., Takahashi, M.: Framed curves in the Euclidean space, Advances in Geometry, 16(3), 265-276 (2016)
- Wang, Y., Pei, D., Gao, R., Generic properties of framed rectifying curves, Mathematics,7, 37 (2019)
- Dogan Yazıcı, B., Özkaldı Karakuş, S., Tosun, M., Framed normal curves in Euclidean space, Tbilisi Mathematical Journal, 27-37 (2019)
- Honda, S., Takahashi, M., Evolutes and focal surfaces of framed immersions in the Euclidean space, Proceedings of the Royal Society of Edinburgh Sect. A., 150(1), 497-516 (2019)
- Fukunaga, T., Takahashi, M., Existence conditions of framed curves for smooth curves, Journal of Geometry, 108, 763-774 (2017)
- Honda, S., Rectifying developable surfaces of framed base curves and framed helices, Advanced Studies in Pure Mathematics, 78, 273-292 (2018)
- Deshmukh, S., Chen B.Y., Turki, N.B.: A differential equations for Frenet curves in Euclidean 3-space and its applications. Rom. J. Math. Comput. Sci, 8(1), 1-6 (2018)
- Chen, B.Y., When does the position vector of a space curve always lie in its rectifying plane?, Amer Math Monthly, 110, 147-152 (2003)
- Chen, B.Y., Dillen, F., Rectifying curves as centrodes and extremal curves. Bull Inst Math Academia Sinica, 33, 77-90 (2005)
- Deshmukh, S., Chen B.Y., Alshammari S.H.: On rectifying curves in Euclidean 3-space, Turk J Math, 42(2), 609-620 (2018)
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Matematik |
| Bölüm | Araştırma Makalesi |
| Yazarlar | |
| Erken Görünüm Tarihi | 30 Nisan 2022 |
| Yayımlanma Tarihi | 30 Nisan 2022 |
| Kabul Tarihi | 2 Temmuz 2021 |
| Yayımlandığı Sayı | Yıl 2022 Cilt: 15 Sayı: 1 |
