Metric (unit)

Pure mathematics

Bundle

Canonical bundle

Mathematics

Sectional curvature

Scalar curvature

Mathematical analysis

Composite material

Economics

Materials science

Curvature

Holomorphic function

Operations management

Geometry

Normal bundle

Vector bundle

Journal of Differential Geometry

We show that if a compact complex manifold admits a Kähler metric whose holomorphic sectional curvature is everywhere non-positive and strictly negative in at least one point, then its canonical bundle is positive. This answers in the affirmative to a question first asked by S.-T. Yau.

Quasi-negative holomorphic sectional curvature and positivity of the canonical bundle