Metrics with cone singularities along normal crossing divisors and   holomorphic tensor fields
  We prove the existence of non-positively curved K\"ahler-Einstein metrics with cone singularities along a given simple normal crossing divisor on a compact K\"ahler manifold, under a technical condition on the cone angles, and we also discuss the case of positively-curved K\"ahler-Einstein metrics with cone singularities. As an application we extend to this setting classical results of Lichnerowicz and Kobayashi on the parallelism and vanishing of appropriate holomorphic tensor fields. 
Fr\'ed\'eric Campana and Henri Guenancia and Mihai P\u{a}un
math.CV math.DG