Acknowledgement
The results presented in this paper were part of the PhD thesis of Bahar Dogan Yazici [17].
References
- C. Boyer, A History of Mathematics, New York, Wiley, 1968.
- J. H. Choi and Y. H. Kim, Associated curves of a Frenet curve and their applications, Appl. Math. Comput. 218 (2012), no. 18, 9116-9124.
- T. Fukunaga and M. Takahashi, Existence conditions of framed curves for smooth curves, J. Geom. 108 (2017), 763-774. https://doi.org/10.1007/s00022-017-0371-5
- T. Fukunaga and M. Takahashi, Framed surfaces in the Euclidean space, Bull. Braz. Math. Soc, New Series, 50 (2019), 37-65. https://doi.org/10.1007/s00574-018-0090-z
- H. H. Hacisalihoglu, Diferensiyel Geometri, Ankara Universitesi Fen Fakultesi, 2000.
- S. Honda and M. Takahashi, Framed curves in the Euclidean space, Adv. Geom. 16 (2016), no. 3, 265-276. https://doi.org/10.1515/advgeom-2015-0035
- S. Honda, Rectifying developable surfaces of framed base curves and framed helices, Adv. Pure Appl. Math. 78 (2018), 273-292. https://doi.org/10.2969/aspm/07810273
- S. Honda, S. Izumiya, and M. Takahashi, Developable surfaces along frontal curves on embedded surfaces, J. Geom. 110 (2019), 27.
- S. Honda and M. Takahashi, Bertrand and Mannheim curves of framed curves in the 3-dimensional Euclidean space, Turk. J. Math. 44 (2020), 883-899. https://doi.org/10.3906/mat-1905-63
- J. Huang and D. Pei, Singularities of non-developable surfaces in three-dimensional Euclidean space, Mathematics, 7 (2019), 1106.
- S. Izumiya and N. Takeuchi, Generic properties of helices and Bertrand curves, J. Geom. 74 (2002), 97-109. https://doi.org/10.1007/PL00012543
- S. Izumiya and N. Takeuchi, Geometry of Ruled Surfaces, In Applicable Mathematics in the Golden Age, 305-338, Misra, J. C., Ed., Narosa Publishing House, New Delhi, India, 2003.
- J. M. Lee, Introduction to Smooth Manifolds-Integral Curves and Flows, Graduate Texts in Math., 205-248, New York, 2003.
- Y. Li, K. Eren, K. H. Ayvaci, and S. Ersoy, The developable surfaces with pointwise 1-type Gauss map of Frenet type framed base curves in Euclidean 3-space, AIMS Math. 8 (2023), 2226-2239.
- H. Liu and F. Wang, Mannheim partner curves in 3-space, J. Geom. 88 (2008), 120-126. https://doi.org/10.1007/s00022-007-1949-0
- S. K. Nurkan, I. A. Guven, and M. K. Karacan, Characterizations of adjoint curves in Euclidean 3-space, Proc. Nat. Acad. Sci. India Sect. A. 89 (2019), no. 1, 155-161.
- B. Dogan Yazici, Ozel Singuler Egrilerin Geometrisi Uzerine, PhD Thesis, Sakarya University, 2022.
- B. Dogan Yazici, O. Z. Okuyucu, and M. Tosun, Framed curves in three-dimensional Lie groups and a Berry phase model, J. Geom. Phys. 182 (2022), 104682.
- B. Dogan Yazici, S. Ozkaldi Karakus, and M. Tosun, On the classification of framed rectifying curves in Euclidean space, Math. Meth. App. Sci. 45 (2022), no. 18, 12089-12098. https://doi.org/10.1002/mma.7561
- B. Dogan Yazici, S. Ozkaldi Karakus, and M. Tosun, Framed Normal Curves in Euclidean Space, TBILISI-MATHEMATICS, 27-37, Sciendo, 2019.
- B. Dogan Yazici, S. Ozkaldi Karakus, and M. Tosun, Framed curves and their applications based on a new differential equation, Int. Electron. J. Geom. 15 (2022), no. 1, 47-56. https://doi.org/10.36890/iejg.875477
- O. G. Yildiz, M. Akyigit, and M. Tosun, On the trajectory ruled surfaces of framed base curves in the Euclidean space, Math. Meth. App. Sci. 44 (2021), no. 9, 7463-7470. https://doi.org/10.1002/mma.6267
- Y. Wang, D. Pei, and R. Gao, Generic properties of framed rectifying curves, Mathematics, 7 (2019), 37.