Stable reflexive sheaves of degree zero on Calabi-Yau manifolds

We give sufficient conditions for the existence of μ-stable reflexive sheaves E on a Calabi-Yau threefold such that the first Chern classes c1(E) satisfy c1(E)⋅H2=0 for some ample line bundle H. We also prove a result concerning deformations to construct rank two μ-stable sheaves on arbitrary smooth projective varieties.