Criterion for existence of a logarithmic connection on a principal bundle over a smooth complex projective variety

Abstract: Let $X$ be a connected smooth complex projective variety of dimension $n \geq 1$. Let $D$ be a simple normal crossing divisor on $X$. Let $G$ be a connected complex Lie group, and $E_G$ a holomorphic principal $G$-bundle on $X$. In this article, we give criterion for existence of a logarithmic connection on $E_G$ singular along $D$.