Curvature growth and holomorphic splitting for Kähler metrics with cone singularities

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