Abstract
It is shown that on a Kahler surface the non-negativity (resp. non-positivity) of the isotropic curvature is implied by the non-negativity (resp. non-positivity) of the holomorphic bisectional curvature. The compact Hermitian surfaces of non-negative isotropic curvature are described. The full list of compact half conformally flat Hermitian surfaces of non-positive isotropic curvature is also given.
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