Metrics with cone singularities along normal crossing divisors and holomorphic tensor fields
Metrics with cone singularities along normal crossing divisors and holomorphic tensor fields
复制标题
沿法向交叉除数和全纯张量场具有锥奇点的度量
DOI：
10.24033/asens.2205
复制
发表时间：
2011
期刊：
影响因子：
--
通讯作者：
Mihai Puaun
中科院分区：
文献类型：
--
作者：
F. Campana;Henri Guenancia;Mihai Puaun
在锥角的技术条件下，证明了紧致K“Ahler流形上沿给定法向交叉因子的锥奇性非正弯曲K”Ahler-Einstein度量的存在性，并讨论了具有锥奇性的正弯曲K“Ahler-Einstein度量的情形.作为应用，我们推广了Lichnerowicz和Kobayashi关于适当全纯张量场的平行度和消失性的经典结果.
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.