  In this paper we provide examples of hypercomplex manifolds which do not
carry HKT structure. We also prove that the existence of HKT structure is not
stable under small deformations. Similarly we provide examples of compact
complex manifolds with vanishing first Chern class which do not admit a
Hermitian structure with restricted holonomy of its Bismut connection in SU(n).
Again we prove that such property is not stable under small deformations.
