TY  - JOUR
T1  - Associated curves from a different point of view in $E^3$
AU  - Canlı, Davut
AU  - Şenyurt, Süleyman
AU  - Ayvacı, Kebire Hilal
PY  - 2022
DA  - September
Y2  - 2022
DO  - 10.31801/cfsuasmas.1026359
JF  - Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics
JO  - Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat.
PB  - Ankara University
WT  - DergiPark
SN  - 1303-5991
SP  - 826
EP  - 845
VL  - 71
IS  - 3
LA  - en
AB  - In this paper, tangent, principal normal and binormal wise associated curves are defined such that each of these vectors of any given curve lies on the osculating, normal and rectifying plane of its partner, respectively. For each associated curve, a new moving frame and the corresponding curvatures are formulated in terms of Frenet frame vectors. In addition to this, the possible solutions for distance functions between the curve and its associated mate are discussed. In particular, it is seen that the involute curves belong to the family of tangent associated curves in general and the Bertrand and the Mannheim curves belong to the principal normal associated curves. Finally, as an application, we present some examples and map a given curve together with its partner and its corresponding moving frame.
KW  - Curve theory
KW  - special curves
KW  - associated curves
KW  - Frenet frame
KW  - Euclidean space
CR  - Bertrand, J., Memoire sur la th´eorie des courbes `a double courbure, Journal de Mathematiques Pures et Appliquees 15 (1850), 332–350.
CR  - Mannheim, A., De l’emploi de la courbe repr´esentative de la surface des normales principales d’une courbe gauche pour la d´emonstration de propri´et´es relatives `a cette courbure, C.R. Comptes Rendus des S´eances de l’Acad´emie des Sciences, 86 (1878), 1254-1256.
CR  - O’Neill, B., Elementary differential geometry, Academic Press Inc., New York, 1966.
CR  - Liu, H., Wang, F., Mannheim partner curves in 3-space, Journal of Geometry 88(1-2) (2008), 120-126. https://doi.org/10.1007/s00022-007-1949-0
CR  - Menninger, T., Characterization of the slant helix as successor curve of the general helix, International Electronic Journal of Geometry, 7(2) (2014), 84-91. https://doi.org/10.36890/iejg.593986
CR  - Kazaz, M., Uğurlu, H. H., Önder, M., Oral, S., Bertrand partner D- curves in the Euclidean 3-space $E^3$, Afyon Kocatepe University Journal of Science and Engineering, 16(1) (2016),
76-83. https://doi.org/10.5578/fmbd.25270
CR  - Kaya, O., Önder, M., New partner curves in the Euclidean 3-space, International Journal of Geometry 6(2) (2017), 41-50.
CR  - Kaya, O., Önder, M., C-partner curves and their applications, Differential Geometry-Dynamical Systems 19 (2017), 64-74.
CR  - Körpınar, T., Sarıaydın, M. T., Turhan, E., Associated curves according to Bishop frame in Euclidean 3 space, Advanced Modeling and Optimization, 15(3) (2013), 713-717.
CR  - Masal, M., Azak, A. Z., Mannheim B-curves in the Euclidean 3-space $E^3$, Kuwait Journal of Science, 44(1) (2017), 36-41.
CR  - Yılmaz, B., Has, A., Alternative partner curves in the Euclidean 3-space, Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 69(1) (2020),
900-909. https://doi.org/10.31801/cfsuasmas.538177
CR  - Choi, J. H., Kim, Y. H., Associated curves of a Frenet curve and their applications, Applied Mathematics and Computation, 218(18) (2012), 9116-9124. https://doi.org/10.1016/j.amc.2012.02.064
CR  - Şahiner, B., Direction curves of principal normal indicatrix of a curve, Journal of Technical Sciences, 8(2) (2018), 46-54.
CR  - Şahiner, B., Direction curves of tangent indicatrix of a curve, Applied Mathematics and Computation, 343 (2019), 273-284. https://doi.org/10.1016/j.amc.2018.09.021
UR  - https://doi.org/10.31801/cfsuasmas.1026359
L1  - https://dergipark.org.tr/en/download/article-file/2091684
ER  -