On the Total CR Twist of Transversal Curves in the 3-Sphere

Abstract

We investigate the total CR twist functional on transversal curves in the standard CR 3-sphere S3⊂C2. The question of the integration by quadratures of the critical curves and the problem of the existence and properties of closed critical curves are addressed. A procedure for the explicit integration of general critical curves is provided, and a characterization of closed curves within a specific class of general critical curves is given. Experimental evidence of the existence of an infinite countable number of closed critical curves is provided.