Asil, Vedat; Körpınar, Talat Construction of inextensible flows of dual normal surfaces in the dual space \(\mathbb D^3\). (English) Zbl 1413.53005 Bol. Soc. Parana. Mat. (3) 31, No. 2, 31-37 (2013). Summary: In this paper, we study dual normal surfaces in dual space Wikipedia Wikipedia Wikipedia Wolfram MathWorld Wolfram MathWorld \(\mathbb D^3\). We research inextensible flows of dual normal surfaces of dual curves in dual space \(\mathbb D^3\). MSC: 53A04 Curves in Euclidean and related spaces 53A05 Surfaces in Euclidean and related spaces Keywords:dual space curve; inextensible flows; structural mechanics; dual Frenet frame × Cite Format Result Cite Review PDF Full Text: Link References: [1] V. Asil, T. Körpınar and E. Turhan: On Inextensible Flows Of Tangent Developable of Biharmonic B-Slant Helices according to Bishop Frames in the Special 3-Dimensional Kenmotsu Manifold,Bol. Soc. Paran. Mat. 31 (1) (2013), 89-97. · Zbl 1413.53067 [2] R. A. Abdel-Baky, R. A. Al-Ghefari: On the one-parameter dual spherical motions, Computer Aided Geometric Design 28 (2011), 23-37. · Zbl 1218.65020 [3] M.P. Carmo: Differential Geometry of Curves and Surfaces, Pearson Education, 1976. · Zbl 0326.53001 [4] B. Y. Chen: Some open problems and conjectures on submanifolds of finite type, Soochow J. Math. 17 (1991), 169-188. · Zbl 0749.53037 [5] T. Körpınar and S. Bas: On Characterization Of B- Focal Curves In E3,Bol. Soc. Paran. Mat. 31 (1) (2013), 175-178. · Zbl 1413.53007 [6] T. Körpınar and E. Turhan: Biharmonic S-Curves According to Sabban Frame in Heisenberg Group Heis3,Bol. Soc. Paran. Mat. 31 (1) (2013), 205-211. · Zbl 1413.53008 [7] T. Körpınar, V. Asil, S. Baş: Characterizing Inextensible Flows of Timelike Curves According to Bishop Frame in Minkowski Space,Journal of Vectorial Relativity Vol 5 (4) (2010), 18-25. [8] T. Körpınar and E. Turhan: On Spacelike Biharmonic Slant Helices According to Bishop Frame in the Lorentzian Group of Rigid Motions E(1, 1), Bol. Soc. Paran. Mat. 30 (2) (2012), 91-100. · Zbl 1413.53048 [9] DY. Kwon , FC. Park, DP Chi: Inextensible flows of curves and developable surfaces, Appl. Math. Lett. 18 (2005), 1156-1162. · Zbl 1085.53058 [10] A. W. Nutbourne and R. R. Martin: Differential Geometry Applied to the Design of Curves and Surfaces, Ellis Horwood, Chichester, UK, 1988. [11] D. J. Struik: Differential geometry, Second ed., Addison-Wesley, Reading, Massachusetts, 1961. · Zbl 0105.14707 [12] S. Bas and T. Körpınar: Inextensible Flows of Spacelike Curves on Spacelike Surfaces according to Darboux Frame in M13, Bol. Soc. Paran. Mat. 31 (2) (2013), 9-17. · Zbl 1413.53028 [13] E. Turhan and T. Körpınar: Parametric equations of general helices in the sol space Sol3, Bol. Soc. Paran. Mat. 31 (1) (2013), 99-104. · Zbl 1413.53016 [14] C.E. Weatherburn: Differential Geometry of Three Dimensions, Vol. I, Cambridge University Press, Cambridge, 1927. · JFM 53.0658.08 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.