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We generalize a result of Heath-Brown and Skorobogatov [Rational solutions of certain equations involving norms,  Acta Math.  189  (2002), 161–177] to show that a certain class of varieties over a number field  k  satisfies Weak Approximation and the Hasse Principle, provided there is no Brauer–Manin obstruction.

A NOTE ON A THEOREM OF HEATH-BROWN AND SKOROBOGATOV