Curvature growth and holomorphic splitting for Kähler metrics with cone singularities

RESUMO

We study Kähler metrics with cone angle $2\pi\beta$ along a smooth divisor, in the range $1/2<\beta<1$. We show that bounded Riemann curvature near the divisor forces the normal bundle sequence to split holomorphically, confirming a condition proposed by Donaldson.