In this study, the normal vector and the unit Darboux vector of spatial involute curve of the spatial quaternionic curve are taken as the position vector, the curvature and torsion of obtained smarandahce curve were calculeted.Mathematics Subject Classification. 53A04, 53C26.

In this paper, we investigate the Smarandache curves according to Sabban frame of fixed pole curve which drawn by the unit Darboux vector of the Bertrand partner curve. Some results have been obtained. These results were expressed as the depends Bertrand curve.

In this paper, we investigated special Smarandache curves in terms of Sabban frame drawn on the surface of the sphere by the unit Darboux vector of involute curve. We created Sabban frame belonging to this curve. It was explained Smarandache curves position vector is composed by Sabban vectors belonging to this curve. Then, we calculated geodesic curvatures of this Smarandache curves. Found results were expressed depending on the base curve. We also gave example belonging to the results found.

No abstract

In this paper, we investigate special Smarandache curves with regard to Sabban frame for Bertrand partner curve spherical indicatrix. Some results have been obtained. These results were expressed depending on the Bertrand curve. Besides, we are given examples of our results.

In this paper, we investigate special Smarandache curves with regard to Sabban frame of involute curve. We create Sabban frame belonging to spherical indicatrix of involute curve. Smarandache curves are explained by Sabban vectors belonging to spherical indicatrix. Then, we calculate geodesic curvatures of this Smarandache curves. The results found for each curve is given depending on evolute curve. The example related to the subject is given and their figures are drawn with MAPPLE program.

In this paper, we investigate special Smarandache curves according to Sabban frame, using the idea of Mannheim partner curve of spherical indicatrix. We created Sabban frame by means of Mannheim partner curve of spherical indicatrix. We explained that position vectors of a Smarandache curves are consisted by Sabban frame given above. Then we calculated geodesic curvatures of this Smarandache curve and the results which we found after calculations are expressed by means of Mannheim partner curve of spherical indicatrix.

Özet: (γ, γ * ) uzaysal kuaterniyonik Bertrand egri çifti verildiginde γ * egrisine ait Frenet vektörlerinin hareketine baglı olarak oluşan w * birim Darboux vektörü ile n * 1 aslinormal vektörü konum vektörü olarak alındıgında bu vektörün çizdigi β = 1 √ 2 (w * + n * 1 ) Smarandache egrisinin, Frenet vektörleri, egriligi ve burulması hesaplandı. Daha sonra bulunan bu egrilik ve burulma uzaysal kuaterniyonik Bertrand egrisine baglı olarak ifade edildi. Konuya örnek verilip Maple programıyla çizimi yapıldı. n * 1 w * -Smarandache Curve According to Frenet Frame of Spatial Quaternionic Bertrand Pair Curves