We consider complex projective space P^{ n} and a smooth closed curve gamma in P^{ n}. Harvey and Lawson have defined the notion of the projective hull \hat{ K} of a compact subset K in P^n. This concept is an analogue of the polynomial hull of compact subsets of C^{ n}. In the present note we study the relation between the following two properties of the curve gamma: (1) \hat{ gamma} - gamma is a one-dimensional complex analytic subvariety of P^{ n} - gamma, and (2) There exists a Stein subdomain of P^{ n} which contains the projective hull \hat{ gamma} of gamma.
Categories: math.CV math.DG