| Résume | Let E → X be a vector bundle of rank r over a compact complex manifold X of dimension n. It is known that if the line bundle \(O_{P (E*)}(1)\) over the projectivized bundle P (E*) is positive, then E ⊗ det E is Nakano positive by the work of Berndtsson. In this talk, we give a subharmonic analogue. Let p : P (E*) → X be the projection and α be a Kähler form on X. If the line bundle \(O_{P (E*)}(1)\) admits a metric h with curvature Θ positive on every fiber and \(Θ^r ∧ p^*α^{n−1} > 0\), then E ⊗ det E carries a Hermitian metric whose mean curvature is positive. As an application, we show that the following subharmonic analogue of the Griffiths conjecture is true: if the line bundle \(O_{P (E*)}(1)\) admits a metric h with curvature Θ positive on every fiber and \(Θ^r ∧ p^*α^{n−1} > 0\), then E carries a Hermitian metric with positive mean curvature. |
