Abstract
References
- 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)
Abstract
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.
Keywords
framed curves framed spherical curves framed helices framed rectifying curves singular points
References
- 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)
Details
| Primary Language | English |
|---|---|
| Subjects | Mathematical Sciences |
| Journal Section | Research Article |
| Authors | |
| Publication Date | April 30, 2022 |
| Acceptance Date | July 2, 2021 |
| Published in Issue | Year 2022 |