Total Torsion and Spherical Curves Bending

It is well known that the total torsion of a closed spherical curve is zero. Furthermore, if the total torsion of any closed curve on the surface is zero, then it is part of a plane or a sphere. In this paper, we examine the total torsion of a spherical curve during infinitesimal bending. We find the appropriate bending fields and show that the variation of the total torsion of a closed spherical curve is equal to zero. Some examples are considered both analytically and using our own software tool. For figures, we use colors to represent the value of torsion at different points of the curve, together with a colour-value scale.