Bertrand and Mannheim partner -curves on parallel surfaces
Resumen
In this paper we study Bertrand and Mannheim partner -curves on parallel surface. Using the definition of parallel surfaces, first we find images of two curves lying on two different surfaces and satisfying the conditions to be Bertrand partner -curve or Mannheim partner -curve. Then we obtain relationships between Bertrand and Mannheim partner -curves and their image curves.
Descargas
Citas
Craig, T., Note on Parallel Surfaces, Journal Für Die Reine und Angewandte Mathematik (Crelle’s Journal), 94, 162-170 (1883).
Ekmekçi, N., Ilarslan, K., On the Bertrand curves and Their Characterizations, Differential Geometry-Dynamical System, Vol. 3, No. 2, 17-24 (2001).
Görgülü, E., Ozdamar, E., A generalizations of the Bertrand curves as general inclined curves in En, Communications de PersonNameProductIDla Fac. Sci.la Fac. Sci. Uni. Ankara, Series A1, 35, 53-60 (1986).
Izumiya, S., Takeuchi, N., Generic properties of helices and Bertrand curves, Journal of Geometry, 74, 97–109 (2002).
Kahraman, T., Önder, M., Kazaz, M., Ugurlu, H.H., Some Characterizations of Mannheim Partner Curves in Minkowski 3-space, Proceedings of the Estonian Academy of Sciences, 60, 4, 210–220 (2011).
Kazaz, M., Ugurlu, H.H., Önder, M., Kahraman, T., Mannheim Partner D-Curves in Euclidean 3-space E3, New Trends in Mathematical Sciences, 3(2) (2015) 24-35.
Kazaz, M., Ugurlu, H.H., Önder, M., Oral, S., Bertrand Partner D-curves in Euclidean 3-space, arXiv:1003.2044v3 [math.DG], 6 May 2010.
Kazaz, M., Ugurlu, H.H., Önder, M., Kahraman, T., Mannheim Partner D-Curves in Minkowski 3-space, arXiv:1003.2043v3 [math.DG], 6 May 2010.
Kazaz, M., Ugurlu, H.H., Önder, M., Oral, S., Bertrand Partner D-curves in the Minkowski 3-space E31, Mathematical Sciences and Applications E-notes, 2(1) 68âAS82 (2014).
Liu, H., Wang, F., Mannheim partner curves in 3-space, Journal of Geometry, Vol. 88, No. 1-2, 120-126 (2008).
O’Neill, B., Elementary Differential Geometry Academic Press Inc. New York, (1966).
Orbay, K., Kasap, E., On Mannheim Partner Curves in E3, International Journal of Physical Sciences, Vol. 4(3.5), 261-264 (2009).
Önder, M., Kiziltug, S., Bertrand and Mannheim Partner D-Curves on Parallel surfaces in Minkowski 3-space, International Journal of Geometry, Vol. 1, No. 2, 31 – 42 (2012)
Struik, D.J., Lectures on Classical Differential Geometry, 2nd ed. Addison Wesley, Dover, (1988).
Tarakçi, Ö., Kiziltug, S., Yayli, Y., On the curves lying on parallel surfaces in the Euclidean 3-space E3, Journal of Advanced Research in Dynamical and Control Systems, Vol. 5, Issue. 3, 26–35 (2013).
Wang, F., Liu, H., Mannheim partner curves in 3-Euclidean space, Mathematics in Practice and Theory, Vol. 37, no. 1, 141-143 (2007).
When the manuscript is accepted for publication, the authors agree automatically to transfer the copyright to the (SPM).
The journal utilize the Creative Common Attribution (CC-BY 4.0).