2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/65411It is known that the properties of almost all points of R^n being not very well (multiplicatively) approximable are inherited by nondegenerate in R^n (read: not contained in a proper affine subspace) smooth submanifolds. In this paper we consider submanifolds which are contained in proper affine subspaces, and prove that the aforementioned diophantine properties pass from a subspace to its nondegenerate submanifold. The proofs are based on a correspondence between multidimensional diophantine approximation and dynamics of lattices in Euclidean spaces.26 pages. To appear in Geom. Funct. Anal. Several misprints correctedNumber TheoryDynamical Systems11J83text