Hyperbolic unitals in the Hall planes

Using the transformation tecnique introduced in [P. Quattrocchi, L.A. Rosati "Transformation of designs and other incidence structres" Geom. Ded. (1992), 233-240], some sufficient conditions to transform a unital embedded in a projective plane into another one are given. As application unitals in the Hall planes are constructed by transformation of the hermitian curves. Necessary and sufficient conditions for the constructed unitals to be projectively equivalent are given too and fferent classes of not projectively equivalent Buekenhout's unitals are found in this manner. The unital of Gruning in the Hall plane is reconstructed and its embeddability in the dual of the Hall plane is also proved. Finally it is proved that the affine unital associated to the unital of Gruning is ismorphic to the hyperbolic hermitian curve.