On the differential geometric elements of bertrandian darboux ruled surface in 3 E

In this paper, we consider two special ruled surfaces associated to a Bertrand curve  and Bertrand mate   . First, Bertrandian Darboux Ruled surface with the base curve  has been defined and examined in terms of the FrenetSerret apparatus of the curve  , in 3 E . Later, the differential geometric elements such as, Weingarten map S, Gaussian curvature K and mean curvature H, of Bertrandian Darboux Ruled the surface and Darboux ruled surface has been examined relative to each other. Further, first, second and third fundamental forms of Bertrandian Darboux Ruled surface have been investigated in terms of the Frenet apparatus of Bertrand curve  , too.

Öklid uzayında bertrandian darboux regle yüzeyin diferensiyel geometrik elemanlar

Bu çalışmada Bertrand eğrisi ve Bertrand eşi olan eğriler üzerinde Darboux vektörleri ile üretilen iki özel regle yüzeyi gözönüne alındı. İlk olarak,  eğrisinin Bertrand Darboux regle yüzeyi, Bertrand eğrisinin Frenet-Serret aparatlar cinsinden tanımlandı ve araştırıldı. Daha sonra, Bertrand Darboux regle yüzeyi ile Darboux regle yüzeyinin Weingarten dönüşümü, Gauss eğriliği ve ortalama eğriliği gibi diferensiyel geometrik değişmezleri birbirleri ile ilişkili olarak incelendi. Son olarak, Bertrand Darboux regle yüzeyinin birinci, ikinci ve üçüncü temel formlar  Bertrand eğrisinin Frenet-Serret aparatlar cinsinden ifadeleri verildi.

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