Classical Differential Geometry of Curves According to Type-2 Bishop Trihedra

In this work, we study classical differential geometry of the curves according to type-2 Bishop trihedra. First, we present some characterizations of a general helix, a helix, special cases and spherical curves. Thereafter, we investigate position vector of a regular curve by a system of ordinary differential equations whose solution gives the components of the position vector with respect to type-2 Bishop frame. Next we prove that the first vector field of the type-2 Bishop frame of a regular curve satisfies a vector differential equation of third order. Solutions of the mentioned system and vector differential equation have not been found. Therefore we present some special characterizations introducing special planes of three dimensional Euclidean space.