On weighted complex Randers metrics (Q645086)

Let \((M, h)\) be a Hermitian manifold and \(\{B_i\}\) a series of holomorphic forms of weights \(i\) on \(M\). Then, a weighted complex Randers metric \(F\) can be constructed with these objects. A main result of the paper under review is that the holomorphic sectional curvature of \(F\) is always less or equal to the holomorphic sectional curvature of \(h\). An important consequence is the following rigidity result: A compact complex manifold of complex dimension \(n\) with a weighted complex Randers metric of positive constant holomorphic sectional curvature is isomorphic with \(\mathbb{P}^n\).