The tubular surfaces generated by great circular surfaces in the three-sphere

We construct a tubular surface generated by a great circular surface in the three-sphere. This tubular surface is the great circular surface when the radius function is equal to 1. We then compute the conditions for the regular tubular surface to be extrinsic flat or minimal. We also study the geodesic curves on both the regular tubular surface. Additionally, we investigate the singular points of the tubular surfaces and have the conditions for a tubular surface and great circular surface be cross-cap.