CURVES AND SURFACES OF AW(k) TYPE

Abstract

In the present study we consider curves and surfaces of AW(k) ( k =1, 2 or 3 ) type. We also give related examples of curves and surfaces satisfying AW(k) type conditions.

Big data mining and business intelligence trends

“…Some companies failed to resolve Big Data. Due to the lack of management "Big Data" processes, they experience trouble in detecting their security flaws as well (Arslan, 2013).…”

Some new properties of null curves on 3-null cone and unit semi-Euclidean 3-spheres

“…Arslan and C.Özgür defined AW(k)-type submanifolds and discussed AW(k)-type curves in Euclidean space [1,18]; M. Külahcı et al studied the spacelike curves of AW(k)-type on 3-null cone [14]; recently, the current authors have spread the AW(k)-type theory to null Cartan curves in Minkowski space [23]. On the other hand, it should be noted that most papers and books on AW(k)-type null curves in Minkowski space.…”

Bertrand curves of AW(k)-type in Lorentzian space

“…A regular curve γ : I ⊆ I R → L n is called a W-curve of rank d, if γ is a Frenet curve of osculating order d and the Frenet curvatures κ i , 1 ≤ i ≤ d − 1 are non-zero constants [2].…”

“…Frenet curves (of osculating order 3) are (see [2]) (i) of type AW(1) if they satisfy N 3 (s) = 0, ii) of type AW(2) if they satisfy…”

“…Many interesting results on curves of AW(k)-type have been obtained by many mathematicians (see [2][3][4]). For example, in [3],Özgür and Gezgin studied a Bertrand curve of AW(k)-type and furthermore, they showed that there was no such Bertrand curve of AW(1)-type and γ was of AW(3)-type if and only if it was a right circular helix.…”