Log-Conformal Projective Manifolds

Let $(X,Δ)$ be a smooth complex projective simple normal crossing pair of dimension $n\ge 3$ endowed with an everywhere nondegenerate logarithmic conformal tensor. If $K_X+Δ$ is not nef, then exactly one of the following occurs: $Δ=\varnothing$ and $X\simeq Q^n$; $X\simeq\mathbb{P}^n$ and $Δ$ is a h