The ruled surface obtained by the natural mate curve
DOI:
https://doi.org/10.5269/bspm.51670Abstract
The natural mate curve r1 of r is deï¬ned the integral of principal normal vector with any parameter s, of a curve r. We investigate the ruled surface generated by the natural mate curve of any Frenet curve r = r(s) in the Euclidean 3-space. We obtained some necessary and sufficient conditions for this surface to be developable and minimal ruled surface. We research related to be the asymptotic curve and the geodesic curve of the base curve on the ruled surface. Example of our main results are also presented.
References
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2. V. Hlavaty. Differentielle Linien Geometrie, P. Nortdhoff, Groningen,( 1945) .
3. Kirson, Y. Curvature theory of in space kinematics, Doctoral dissertation, University of California, Berkley, Calif, USA, (1975).
4. Karadag, H. B., Kılıc, E. & Karadag, M. On the developable ruled surfaces kinematically generated in Minkowski 3-Space. Kuwait Journal of Science 41(1): 21-34, (2014).
5. Deshmukh, S., Chen, B. Y., & Alghanemi, A. Natural mates of Frenet curves in Euclidean 3-space. Turkish Journal of Mathematics, 42(5), 2826-2840, (2018). https://doi.org/10.3906/mat-1712-34
6. Wang, J., Jiang, P., Guo, Y., & Meng, J. Developable surface pencil pairs with special pairs as common asymptotes. Applied Mathematics and Computation, 362, 124583, (2019). https://doi.org/10.1016/j.amc.2019.124583
7. O'Neill, B. Elementary Differential Geometry, Academic Press, New York, 411 pp, (1966). https://doi.org/10.1016/B978-1-4832-3170-9.50011-7
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2022-12-23
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