##### Title: Normal Ruled Surfaces of a Surface along a Curve in Euclidean 3-Space E3

##### Pages: 559-577

##### Cite as:

R. A. Abdel-Baky, S. H. Nazra, Normal Ruled Surfaces of a Surface along a Curve in Euclidean 3-Space E3, Int. J. Anal. Appl., 17 (4) (2019), 559-577.#### Abstract

In this paper, we define a ruled surface normal to a surface along a curve on the surface. Then, we analyze the necessary and sufficient condition for that surface to be normal developable. Also, we solve the problem when the resulting developable surface is a cylinder, cone or tangent surface. Finally, we give some representative examples.

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#### References

- B. O’Neill. Elementary Differential Geometry. Academic Press Inc., New York 1966.
- M.P. Do Carmo. Differential Geometry of Curves and Surfaces. Englewood Cliffs: Prentice Hall, 1976.
- G. Farin. Curves and Surfaces for Computer Aided Geometric Design, 2nd ed. New York: Academic Press, 1990.
- G.J. Wang, K. Tang, and C.L. Tai. Parametric representation of a surface pencil with a common spatial geodesic, Comput.- Aided Des., 36 (2004), 447–459.
- E. Kasap, F.T. Akyildiz, K. Orbay. A generalization of surfaces family with common spatial geodesic, Appl. Math. Comput., 201 (2008), 781–789.
- G. Saffak, E. Kasap. Family of surface with a common null geodesic, Internat. J. Phys. Sci., 4(8) (2009), 428–433.
- C.Y. Li, R.H. Wang, C.G. Zhu. Parametric representation of a surface pencil with a common line of curvature, Comput. Aided Des., 43 (9) (2011), 1110–1117.
- E. Bayram, F. Guler, E. Kasap. Parametric representation of a surface pencil with a common asymptotic curve, Comput. Aided Des., 44 (2012), 637–643.
- C.Y. Li, R.H. Wang, C.G. Zhu. An approach for designing a developable surface through a given line of curvature, Comput. Aided Des., 45 (2013) 621–627.
- G.Y. Senturk, S. Yuce. Characteristic properties of the ruled surface with Darboux frame. Kuwait J. Sci. 42 (2) (2015), 14–33.
- G.Y. Senturk, S. Yuce. Bertrand offsets of ruled surfaces with Darboux Frame, Result. Math. 72 (3) (2017), 1151–1159.