Tubular Surfaces of Adjoint Curves According to the Modified Orthogonal Frame

In this paper, we study tubular surfaces defined by adjoint curves which have a wide range of applications. In three-dimensional Euclidean space, we consider tubular surfaces in modified orthogonal frame generated by a curve β whose center curve is adjoint of a curve α. We give some characterizations for tubular surfaces constructed according to with curvature and with torsion modified orthogonal frames. Through these characterizations we obtain some important results. We also study asymptotic and geodesic curves as well as flat, minimal, Weingarten and linear-Weingarten surfaces using conventional differential geometry techniques. Finally, we present case examples for both versions of the frame to validate our theoretical results.