Hermitian surfaces of constant holomorphic sectional curvature (Q909262)

\textit{A. Balas} and \textit{P. Gauduchon} have studied compact Hermitian surfaces of constant holomorphic sectional curvature with respect to the Hermitian connection (known also as the Chern connection) [Math. Z. 190, 39-43 (1985; Zbl 0549.53063)]. It is observed that the constancy of the holomorphic sectional curvature with respect to the Hermitian connection does not necessarily mean the constancy of the holomorphic sectional curvature with respect to the Riemannian connection. In the present paper, the authors study the structure of compact Hermitian surfaces of constant holomorphic sectional curvature with respect to the Riemannian connection and show the corresponding results to the ones due to A. Balas and P. Gauduchon.