A remark on compact balanced threefolds with constant holomorphic sectional curvature

Abstract

Motivated by a recent work of Zhou-Zheng [20], we study compact balanced threefolds with constant holomorphic sectional curvature with respect to the Chern connection. We prove that a compact normal balanced threefold with constant holomorphic sectional curvature is Kähler if the constant is negative and Chern flat when the constant is zero.