The differential geometry of curves in Rossi sphere

The Rossi sphere is a nonembeddable CR manifold. The differential geometry of curves in the Heisenberg group H1, in the CR sphere, and in the disk bundle B1×R have been studied in the literature by using the p-curvature and T-variation. In this paper, we study the differential geometry of curves in the Rossi sphere. In particular, we prove the fundamental theorem of curves in the Rossi sphere. We also find the explicit formula of the p-curvature and T-variation of curves in the Rossi sphere. As an application, we can classify curves in the Rossi sphere with vanishing p-curvature and T-variation.