Hyperoval constructions on the Hermitian surface

New infinite families of hyperovals of the generalized quadrangle H(3,q2)H(3,q2) are provided. They arise in different geometric contexts. More precisely, we construct hyperovals by means of certain subsets of the projective plane called here k  -tangent arcs with respect to a Hermitian curve (Section 2), hyperovals arising from the geometry of an orthogonal polarity commuting with a unitary polarity (Section 3), hyperovals admitting the irreducible linear group PSL(2,7)PSL(2,7) as a subgroup of PGU(3,q2)PGU(3,q2), q=phq=ph, p≡3,5or6(mod7) and h   an odd integer (Section 4). Finally we construct hyperovals by means of the embedding of PSp(4,q)