``Complex tangential curves of constant curvature in the unit ball of C^2 and homogeneous polynomials'' A. Iordan, Universite' Paris VI (France) ABSTRACT: We prove that a non-constant homogeneous polynomial P on C^2 having the property: P=1 on a complex-tangential real analytic curve of the boundary of the unit ball reduces to a monomial by a unitary change of variables. This is a positive answer to conjectures of H.O.Kim.