This paper considers the global geometry of general low-rank minimization problems via the Burer-Monterio factorization approach. For the rank-1 case, we prove that there is no spurious second-order critical point for both symmetric and asymmetric problems if the rank-2 RIP constant δ is less than 1/2. Combining with a counterexample with δ=1/2, we show that the derived bound is the sharpest possible. For the arbitrary rank-r case, the same property is established when the rank-2r RIP constant δ…