2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/112995Germs of locally homogeneous CR manifolds M can be characterized in terms of certain algebraic data, e.g., by CR-algebras. We give an explicit formula which relates the Levi form of such an M and its higher order analogues to the Lie brackets in certain finite dimensional Lie algebras. As an application we give a simple characterization of geometric properties of M such as minimality, k-nondegeneracy, holomorphic degeneracy etc. in purely algebraic terms. We present an example of a homogeneous 3-nondegenerate CR-manifold. We also determine a universal upper bound for the order k of k-nondegenerate orbits of real forms in flag manifolds.Complex VariablesGroup Theory32V05; 32V35 (primary); 57S25 (secondary)text