The aim of this paper is to study in characteristic $2$ and degree at most $4$ the isotropy of involutions of the first kind and quadratic paires over the function field of a projective quadric. We also give a complete answer to the hyperbolicity over an inseparable quadratic extension in arbitrary degree. The case of a separable quadratic extension has been studied in .
Ahmed Laghribi. "Involutions en degré au plus 4 et corps des fonctions d'une quadrique en caractéristique 2." Bull. Belg. Math. Soc. Simon Stevin 12 (2) 161 - 174, June 2005. https://doi.org/10.36045/bbms/1117805081