Hermitian threefolds with vanishing real bisectional curvature

We examine the class of compact Hermitian manifolds with constant holomorphic sectional curvature. Such are conjectured to be K\"ahler (hence a complex space form) when is non-zero and Chern flat quotient Lie group) zero. The conjecture known in dimension two but open higher dimensions. In this paper, we establish partial solution three by proving that any threefold zero real bisectional curvature must flat. Real notion introduced Xiaokui Yang second named author 2019, generalizing It equivalent latter case slightly stronger general.