Metric Diophantine approximation: The Khintchine--Groshev theorem for   non-degenerate manifolds
  The main objective of this paper is to prove a Khintchine type theorem for divergence for linear Diophantine approximation on non-degenerate manifolds, which completes earlier results for convergence. 
V. Beresnevich, V. Bernik, D. Kleinbock, and G.A. Margulis