TY  - JOUR
T1  - Curves According to the Successor Frame in Euclidean 3-Space
AU  - Masal, Melek
PY  - 2018
DA  - December
Y2  - 2018
DO  - 10.16984/saufenbilder.425519
JF  - Sakarya University Journal of Science
JO  - SAUJS
PB  - Sakarya University
WT  - DergiPark
SN  - 2147-835X
SP  - 1868
EP  - 1873
VL  - 22
IS  - 6
LA  - en
AB  - In thepresent study, the successor formulae of the successor curves defined byMenninger [1] are given. Then, by defining the successor planes, the geometricmeanings of the successor curvatures are investigated and the relations acrossthe components of the position vectors of successor curves are found.Furthermore, in this study, it is proven that lies in the 3rd.type successorplane, lies in the 1st type successorplane and by defining the involute-evolute S-pair, the distance between thecorresponding points of these curves is found.
KW  - Successor frame
KW  - Successor curves
KW  - Slant helix
KW  - Involute-evolute curves
CR  - Menninger, A. (2014) Characterization of the slant helix as successor curves of the general helix. International Electronic Journal of Geometry, 7(2):84-91.
CR  - Ali, A.T. (2011) Position vectors of general helices in Euclidean 3-space. Bull. Math. Analy. Appl. 3 (2): 198-205.
CR  - Bertrand, J. (1850) La theories de courbes a double courbure. J. Math. Pures et Appl. 15: 332-350.
CR  - Do Carmo, M.P. (1976) Differential geometry of curves and surfaces. Prentice Hall, Englewood Cliffs, New Jersey.
CR  - Fuchs, D. (2013) Evolutes and involutes of spatial curves. Amer. Math. Monthly, 120(3):217-231.
CR  - Izumiya, S. & Takeuchi, N. (2002) Generic properties of helices and Bertand curves. J. Geom., 71(1): 97-109.
CR  - Liu, H. & Wang F., (2008) Mannheim partner curves in 3-space. J. Geom., 88: 120-126.
CR  - Lucas, P. & Ortega-Yagues, J.A.,(2012) Bertrand curves in the three-dimensional sphere. J. Geom. Phys., 62(9): 1903-1914.
CR  - Orbay, K. & Kasap, E. (2009) On Mannheim partner curves in    . Int. J. Phys. Sci., 4(5): 261-264.
CR  - Struik, D.J. (1988) Lectures on classical differential geometry. Dover, New-York.
CR  - Bektaş, Ö. & Yüce, S. (2013) Special involute-evolute partner D-curves in. European Journal of Pure and Applied Mathematics, 6(1):20-29.
CR  - Bükcü, B. & Karacan, M.K. (2009) The slant helices according to Bishop frame,.World Academy of Science, Engineering and Technology, 59:1039-1042.
CR  - Yılmaz, S. & Turgut, M. (2010) A new version of Bishop frame and application to spherical images. J. Math. Anal. Appl., 371: 764-776.
UR  - https://doi.org/10.16984/saufenbilder.425519
L1  - https://dergipark.org.tr/en/download/article-file/551930
ER  -