Abstract
It was proved in the paper [KM1] that the properties of almost all points of $ \mathbb{R}^{n} $ being not very well (multiplicatively) approximable are inherited by nondegenerate in $ \mathbb{R}^{n} $ (read: not contained in a proper affine subspace) smooth submanifolds. In this paper we consider submanifolds which are contained in proper a.ne 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.
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