论文标题
最佳符号连接的独特性
Uniqueness of optimal symplectic connections
论文作者
论文摘要
考虑紧凑的kähler歧管之间的全态累积，使每个纤维都接受恒定的标态曲率kähler指标。当纤维接收连续的自动形态时，纤维中的恒定标态曲率Kähler指标的选择并不是唯一的。最佳的符号连接是纤维中的恒定标量曲率kähler度量的选择，满足几何部分偏微分方程。该条件通过诱导的fibrewise fubini-study tudy指标，可以将hermite-instein条件用于霍尔米特 - 因构成载体束。 我们证明了有关最佳符号连接的各种基础分析结果。我们的主要结果证明了最佳的符号连接是独特的，直到存在于沉浸式的自动形态群体的作用。因此，最佳的符号连接是规范相对较大的kähler指标。此外，我们表明，最佳符号连接的存在迫使沉团的自动形态群还原性，并且在该自多态群体的最大紧凑型亚组下，最佳的符号连接会自动不变。我们还证明，当浸没接受最佳的符号连接时，它实现了我们定义的自然对数规范功能的绝对最小值。
Consider a holomorphic submersion between compact Kähler manifolds, such that each fibre admits a constant scalar curvature Kähler metric. When the fibres admit continuous automorphisms, a choice of fibrewise constant scalar curvature Kähler metric is not unique. An optimal symplectic connection is choice of fibrewise constant scalar curvature Kähler metric satisfying a geometric partial differential equation. The condition generalises the Hermite-Einstein condition for a holomorphic vector bundle, through the induced fibrewise Fubini-Study metric on the associated projectivisation. We prove various foundational analytic results concerning optimal symplectic connections. Our main result proves that optimal symplectic connections are unique, up to the action of the automorphism group of the submersion, when they exist. Thus optimal symplectic connections are canonical relatively Kähler metrics when they exist. In addition, we show that the existence of an optimal symplectic connection forces the automorphism group of the submersion to be reductive, and that an optimal symplectic connection is automatically invariant under a maximal compact subgroup of this automorphism group. We also prove that when a submersion admits an optimal symplectic connection, it achieves the absolute minimum of a natural log norm functional which we define.
