On the geodesics of tubular surfaces in Minkowski 3-space
We consider geodesics of tubular surfaces by using two-parameter spatial motion along a curve in Minkowski 3-space. To do this, we solve the differential equation \(\overline D_TT = 0\) of parametric curves on the tubular surface where \(D\) is the connection of the tubular surface and \(T\) is the unit vector field of two parametric curves on the tubular surface in particular. It is shown that for fixed \(s\) all of parametric curves of the tubular surface \(M =\varphi(s,t)\) are geodesics and for fixed \(t\) only the curves \(\varphi_{t = 0}(s)\) are geodesics.
scientific article; zbMATH DE number 5304874