Translation Generalized Quadrangles In Even Characteristic

In this paper, we first introduce new objects called “translation generalized ovals” and “translation generalized ovoids”, and make a thorough study of these objects. We then obtain numerous new characterizations of the $T_{2} {\left( {\user1{\mathcal{O}}} \right)}$ of Tits and the classical generalized quadrangle ${\user1{\mathcal{Q}}}{\left( {4,q} \right)}$ in even characteristic, including the complete classification of 2-transitive generalized ovals for the even case. Next, we prove a new strong characterization theorem for the $T_{3} {\left( {\user1{\mathcal{O}}} \right)}$ of Tits. As a corollary, we obtain a purely geometric proof of a theorem of Johnson on semifield flocks.