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The Generalised Baker-Schmidt Problem (1970) concerns the Hausdorff$f$-measure of the set of $\Psi$-approximable points on a nondegeneratemanifold. We refine and extend our previous work [Int. Math. Res. Not. IMRN2021, no. 12, 8845--8867] in which we settled the problem (for dualapproximation) for hypersurfaces. We verify the GBSP for certain classes ofnondegenerate submanifolds of codimension greater than $1$. Concretely, forcodimension two or three, we provide examples of manifolds where the dependentvariables can be chosen as quadratic forms. Our method requires the manifold tohave even dimension at least the minimum of four and half the dimension of theambient space. We conjecture that these restrictions on the dimension of themanifold are sufficient to provide similar examples in general.

The Baker-Schmidt problem for dual approximation and some classes of functions