Translation ovoids of unitary polar spaces

An ovoid of a finite classical polar space is a set of points having exactly one point in common with every generator. An ovoid is a translation ovoid with respect to one of its points if it admits a collineation group fixing all totally isotropic lines through the point and acting regularly on the remaining points of the ovoid. Lunardon and Polverino proved in [11] that Q+(3, q), Q(4, q) and Q+(5, q) are the only finite orthogonal polar spaces having translation ovoids. In this paper we prove that H(3, q2) is the only finite unitary polar space having translation ovoids. We also prove that translation groups of ovoids of H(3, q2) contain only linear collineations