Union curves in W2 relative to a congruence and union curvature of a curve in W2

Abstract

In this paper, firstly we obtained differential equation of the union curves in W 2. Then, we showed that obtained equation is equivalent to a pair of differential equations of the second order. We denoted it by (η 1 , η 2) and we named η 1 and η 2 as the components of the union curvature vector field. We defined union curves in W 2 relative a congruence by means of the union curvature vector field. Finally, we expressed union curvature of a curve in W 2 in terms of the components of the union curvature vector field.

Union, hyperasymptotic and hypernormal curves in Weyl space

“…where κ g is the geodesic curvature of C [2]. On the other hand, we have κ g = κ u cos ψg ab y 1 a n b + κ u sin ψg ab y 2 a n b = κ u cos ψg ab 1…”