Forms of almost homogeneous varieties over perfect fields

We study the forms of the almost homogeneous varieties. More precisely, we first obtain criteria for the existence of forms in the homogeneous case, and then we extend the Luna-Vust theory over perfect fields to determine whether a given form of the dense open orbit of an almost homogeneous variety comes from a form of the whole variety. Finally, we apply our results to study the real forms of the complex almost homogeneous $\SL_2$-threefolds.