Quasi Focal Curves of Adjoint Curves of Timelike Curves in 3d Minkowski Space

Abstract

In this work, we obtain new results by examining the adjoint curve and focal curve, which are examples of associated curves. In particular, we examine the focal curve of the adjoint curve of a timelike curve we have described with quasi-frame ( Q-frame) elements in 3D Minkowski space M1^3. We first characterize the focal curves of adjoint curves by considering the Q-frame in M1^3 . Next, we determine the focal curvatures of this curve. In the last section, we give some results by obtaining the focal curve in M1^3 in terms of principal curve and adjoint curve.

Some Integral Characterizations of Timelike Helices in R2^4

“…The curves are interpreted geometrically with the help of a frame in different spaces. There are many studies about curves and especially special curves in 4 2 [1][2][3][4][5][6][7]. The semi-Euclidean space 4 2 is the standard vector space given with the metric ,…”