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k-TYPE SLANT HELICES DUE TO GENERALIZED BISHOP FRAME (GBF) OF TYPE C AND TYPE D IN E4
(Palestine Polytechnic University, 2025) Singh, Charan; Kazan, Ahmet; Altın, Mustafa; Kazan, Sema; Jamali, Mohammed
The present article deals with the study of k-type slant helices with two equivalence classes of generalized Bishop frames (GBF) called type C frame and type D frame in E4 and obtain characterizations for such curves with these frames. © Palestine Polytechnic University-PPU 2025.
ON CERTAIN SPACE CURVES DUE TO PARALLEL TRANSPORT FRAME IN En
(Univ Nis, 2025) Singh, Charan; Kazan, Ahmet; Altin, Mustafa; Kazan, Sema; Jamali, Mohammed
In this paper, we study k-type (k is an element of {0, 1, 2, ...., n-1}) slant helices due to non-zero parallel transport frame in E-n. We give some characterizations for 0-type, 1-type,..., and in general (n-1)-type slant helix due to parallel transport frame in terms of parallel transport curvatures in E-n and with the aid of these characterizations we give an important general theorem which gives the necessary and sufficient condition for any space curve to be k-type slant helices due to parallel transport frame in E-n. We also obtain the characterizations of the curves whose position vectors belong to the normal, rectifying and osculating spaces (called normal, rectifying and osculating curves, respectively) due to parallel transport frame in E-n.