TY  - JOUR
T1  - On the singularity and distribution parameters of involutive and Bertrandian Frenet ruled surfaces in E^3
AU  - Kilicoglu, Seyda
AU  - Senyurt, Suleyman
PY  - 2016
DA  - September
JF  - New Trends in Mathematical Sciences
PB  - Mustafa BAYRAM
WT  - DergiPark
SN  - 2147-5520
SP  - 180
EP  - 185
VL  - 4
IS  - 3
LA  - en
AB  - In this paperwe consider twelve special ruled surfaces associated to the curve the involute curve  and Bertrand mate  , with . They are called as Frenet ruled, involutive Frenet ruled and BertrandianFrenet ruled surfaces, cause of their generators are the Frenet vector fieldsof curve . First we give all the parametrizations of all Frenet ruled surfaces interms of the Frenet apparatus of curve  We examined distribution parametersand Singularity of involutive and Bertrand Frenet ruled surfaces based on theFrenet apparatus of curve  in E
KW  - Involute curve
KW  - Bertrand curve pair
KW  - striction curves
KW  - ruled surfaces
CR  - Çalışkan, M. and Bilici, M., Some Characterizations for the pair of Involute-Evolute Curves in Euclidean space E^3, Bulletin of Pure and Applied Sciences, 21(2), 289-294, 2002.
CR  - Do Carmo, M. P., Differential Geometry of Curves and Surfaces, Prentice-Hall, ISBN 0-13-212589-7, 1976.
CR  - Gray, A. Modern Differential Geometry of Curves and Surfaces with Mathematica, 2nd ed. Boca Raton, FL: CRC Press, 205, 1997.
CR  - Hacısalihoğlu H.H., Differential Geometry(in Turkish), vol.1, İnönü Üniversity Publications, 1994.
CR  - Kılıçoğlu Ş, Şenyurt, S. and Hacısalihoğlu H.H., On the striction curves of Involute and Bertrandian Frenet ruled surfaces in E^3, Applied Mathematical Sciences, 9(142), 7081 - 7094, 2015, http://dx.doi.org/10.12988/ams.2015.59606.
CR  - Şenyurt, S., Kılıçoğlu Ş. and Hacısalihoğlu H.H., An Examination on the Positions of Frenet Ruled Surfaces Along Bertrand Pairs α and α^* According to Their Normal Vector Fields in E^3, Applied Mathematical Sciences, 9(142), 7095 - 7103, 2015.
CR  - Izumiya, S., Takeuchi, N., Special curves and Ruled surfaces, Beitrage zur Algebra und Geometrie Contributions to Algebra and Geometry,44(1), 203-212, 2003.
CR  - Schief W., On the integrability of Bertrand curves and Razzaboni surfaces. Journal of Geometry and Physics, Volume 45, Issues 1–2, Pages 130–150, February, 2003.
CR  - Şenyurt, S. and Kılıçoğlu Ş., On the differential geometric elements of the involute D ̃ scroll, Adv. Appl. Cliff ord Algebras 2015 Springer Basel,doi:10.1007/s00006-015-0535-z.
UR  - https://dergipark.org.tr/tr/pub/ntims/issue//519867
L1  - https://dergipark.org.tr/tr/download/article-file/637732
ER  -