Radial Conformal Curves Of Spherical Curves In Euclidean 3-Space

Nowadays lots of ideal and valuable results for curves and the curves on some surfaces have been obtained.In this paper,we base on fundamental theories of space curves in classical differential geometry and use the Frenet and spherical Frenet frames to study the spherical curves in Euclidean 3-space which break the traditional restriction only lying on the Frenet frame.There exists a common class problem that is to establish some point corresponding relationship between two curves in local curves theory.Such kind of correspondence can be understood that both sides are continuous and differentiable and these geometric features meet some certain geometry conditions.Finally by making use of the Frenet formula to calculus process,the corresponding analytical expressions can be obtain which are the relationship between the curve and its corresponding curve.Motivated by this idea,we defined the radial conformal curve of a spherical curve and studied their corresponding relationship in Euclidean 3-space.It is well known that the curvature and torsion can decide a space curve completely except the location of the curve which are powerful tools to study curves.Everything is clear once we find out the corresponding relationship between the curvature and torsion of the radial conformal curve and its spherical curve.In addition,the result is general which can be applied to other special curves.