A note on holomorphic sectional curvature of a hermitian manifold. (4th September 2022) - Li, Hongjun; Qiu, Chunhui
Abstract: As is well known, the holomorphic sectional curvature is just half of the sectional curvature in a holomorphic plane section on a Kähler manifold (Zheng, Complex differential geometry (2000)). In this article, we prove that if the holomorphic sectional curvature is half of the sectional curvature in a holomorphic plane section on a Hermitian manifold then the Hermitian metric is Kähler.