Tosun, Ceyda; Kocayigit, Huseyin; Aydin, Tuba agirman

In this study, a new class of surface curves, namely Yi-Darboux slant helices, is investigated. The conditions under which a surface curve is a iY-Darboux slant helix with respect to the Osculating Darboux (OD), Normal Darboux (ND), and Rectifying Darboux (RD) frames are established, and several characterizations are obtained. In particular, necessary and sufficient conditions are derived in terms of the curvature functions associated with these frames. Furthermore, relationships between iY-Darboux slant helices and classical helices and slant helices are established for special surface curves, including geodesics, asymptotic curves, and lines of curvature. Concrete examples on conical and cylindrical surfaces are also presented to illustrate the theoretical results.

İncele

Aydin, Tuba Agirman; Ayazoglu, Rabil; Kocayigit, Huseyin

In this paper, we define timelike curves in R-2(4) and characterize such curves in terms of Frenet frame. Also, we examine the timelike helices of R-2(4), taking into account their curvatures. In addition, we study timelike slant helices, timelike B-1-slant helices, timelike B-2-slant helices in four dimensional semi-Euclidean space, R-2(4). And then we obtain an approximate solution for the timelike B-1 slant helix with Taylor matrix collocation method.

AtıfWoS1

İncele

Balki Okullu, Pinar; Kocayigit, Huseyin; Agirman Aydin, Tuba

In this paper, spherical curves are studied by using Bishop frame. First, the differential equation characterizing the spherical curves is given. Then, we exhibit that the position vector of a curve which is lying on a sphere satisfies a third-order linear differential equation. Then we solve this linear differential equation by using Bernstein series solution method.

AtıfScopus2·OpenAlex1

İncele