论文标题
退化的Hermitian几何形状和全态纤维的曲率
Degenerate Hermitian geometry and curvatures of holomorphic fibrations
论文作者
论文摘要
我们计算了全体形态纤维的总空间上的指标曲率张量。我们的主要工具是Chern连接和曲率形式的理论，该理论可能会在霍明型载体束上退化的冬宫形式。我们证明了Codazzi-Griffiths方程的一个版本，用于该环境中子和商捆绑包的曲线，并将其应用于对振动的诚实赫米尔人指标的研究。我们将其应用于计算格拉曼尼亚束上的度量标准的曲率，并证明它们具有正构形截面曲率，如果底座为基础。
We calculate curvature tensors of metrics on the total spaces of holomorphic fibrations. Our main tool is a theory of Chern connections and curvature forms for possibly degenerate Hermitian forms on holomorphic vector bundles. We prove a version of the Codazzi-Griffiths equations for curvatures of sub- and quotient bundles in that setting and apply them to the study of honest Hermitian metrics on fibrations. We apply this to calculate the curvature of a metric on Grassmannian bundles and prove they have positive holomorphic sectional curvature if the base does.
