Mean curvature of direct image bundles

2025/08/01 by Kuang-Ru Wu, Wu, Kuang-Ru · 1 citation
Mathematics · #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2508.00820

openalex publication_date 2025/08/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 paper, 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\wedge 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\wedge p^*α^n-1> 0, then E carries a Hermitian metric with positive mean curvature.

Citations

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• Uniform RC-positivity of direct image bundles

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