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 of Tits and the classical generalized quadrangle 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 of Tits. As a corollary, we obtain a purely geometric proof of a theorem of Johnson on semifield flocks. * The second author is a Postdoctoral Fellow of the Fund for Scientific Research—Flanders (Belgium).