TY - JOUR T1 - R^2 de Bir n-li Eğri Ailesinin Afin Diferansiyel İnvaryantları TT - Affine Differential Invariants of a Family of n Curves in R^2 AU - Gözütok, Uğur AU - Sağıroğlu, Yasemin PY - 2018 DA - June Y2 - 2018 DO - 10.16984/saufenbilder.341517 JF - Sakarya University Journal of Science JO - SAUJS PB - Sakarya University WT - DergiPark SN - 2147-835X SP - 1007 EP - 1014 VL - 22 IS - 3 LA - tr AB - Bu çalışmada tane eğrinin üreteç diferansiyel invaryantlarıbelirlenmiş olup, bu üreteç kümesinin fonksiyonel bağımsız olduğugösterilmiştir. Ayrıca bu diferansiyel invaryantlar kullanılarak de iki tane lieğri ailesinin denklik problemi araştırılmıştır. KW - afin diferansiyel geometri KW - invaryant KW - eğriler N2 - In thisstudy, we determine generating differential invariants for curves, which is shown to be fonctionallyindependent. In addition, using these diffenrial invariants, the equivalenceproblem of two families of curves in is investigated. CR - R.G. Aripov, D. Khadjiev, The Complete system of global differential and integral invariants of a curve in Euclidean geometry, Russian Mathematics, vol. 51, no. 7, pp. 1-14, 2007. CR - W. Blaschke, Affine Differentialgeometrie, Springer, Berlin, 1923. CR - R.B. Gardner, G.R. Wilkens, The fundamental theorems of curves and hypersurfaces in centro-affine geometry, Bull. Belg. Math. Soc., vol. 4, pp. 379-401, 1997. CR - S. Izumiya, T. Sano, Generic afine differential geometry of space curves, Proceedings of the Royal Society of Edinburg, vol. 128, no. A, pp. 301-314, 1998. CR - D. Khadjiev, The Application of Invariant Theory to Differential Geometry of Curves. Fan Publ, Tashkent, 1988. CR - D. Khadjiev, Ö. Pekşen, The Complete system of global differential and integral invariants for equi-affine curves, Differential Geom. Appl., vol. 20, pp. 167-175, 2004. CR - H. Liu, Curves in affine and semi-Euclidean Spaces, Result. Math., vol. 65, pp. 235-249, 2014. CR - Y. Sağıroğlu, Affine Differential Invariants of Curves: The Equivalence of Parametric Curves in Terms of Invariants. LAP LAMBERT Academic Publishing, 2012. CR - Y. Sağıroğlu, The Equivalence problem for parametric curves in one-dimensional affine space, Int. Math. Forum, vol. 6, no. 4, pp. 177-184, 2011. CR - P.A. Schirokow, A.P. Schirokow, Affine Differentialgeometrie, Teubner, Leipzig, 1962. CR - B. Su, Affine Differential Geometry, Science Press, Beijing, 1983. UR - https://doi.org/10.16984/saufenbilder.341517 L1 - https://dergipark.org.tr/en/download/article-file/477608 ER -