Spherical Indicatrices of Involute of a Space Curve in Euclidean 3-Space
In this work, we studied the properties of the spherical indicatrices of involute curve of a space curve and presented some characteristic properties in the cases that involute curve and evolute curve are slant helices and helices, spherical indicatrices are slant helices and helices and we introduced new representations of spherical indicatrices.
F.Wang and H. Liu, Mannheim Partner Curve in 3-Euclidean Space, Mat hematics in Practice and Theory, 37 (2007), 141-143.
H. Liu and F. Wang, Mannheim Partner Curve in 3-Space, Journal of Geometry, 88 (2008),120-126.
H. Matsuda and S. Yorozu, Notes on Bertrand Curves, Yokohama Math. J., 50 (2003), 41-58.
J. Monterde,Curves with constant curvature ratios, Bol. Soc. Math. Mexicana (3) 13, no.1 (2007),177-186.
L. Kula and Y. Yayli, On slant helix and its spherical indicatrix, Applied Mathematics and Computation, 169 (2005), 600-607.
L. Kula, N. Ekmekci, Y. Yayli and K. _Ilarslan, Characterizations of slant Helices in Euclidean 3-Space, Turk J. Math. 34 (2010), 261-273.
M.P. Carmo, Differential Geometry of Curves and Surfaces, Prentice-Hall, New Jersey, 1976.
S. Izumiya and N. Takeuchi, New Special Curves and Developable Surfaces, Turk. J. Math., 28 (2004), 153-164.
Copyright (c) 2020 Tamkang Journal of Mathematics
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.