论文标题
在相对较为kähler指标的空间中的大地测量学
Geodesics in the space of relatively Kähler metrics
论文作者
论文摘要
我们在纤维上得出相对kähler指标的地理方程，并证明具有纤维恒定标态曲率的任何两个这样的指标都与独特的平滑测量线相连。然后，我们显示了沿测量学沿该设置的对数正常功能的凸度，从而产生了Dervan和Sektnan的独特性结果的简单证明，以实现最佳的符号连接以及对数字函数的界限结果。接下来，我们将纤维化变性与在密集的开放子集上定义的独特的大地射线相关联。计算沿全球定义的平滑测量光线的对数正常函数的限制斜率，我们证明，对于一大群在基础上平滑的纤维纤维变性，允许最佳符号连接的纤维化是一值的。在项目活动的载体束和各向同性振动的情况下，我们提供了这种退化的例子。
We derive the geodesic equation for relatively Kähler metrics on fibrations and prove that any two such metrics with fibrewise constant scalar curvature are joined by a unique smooth geodesic. We then show convexity of the log-norm functional for this setting along geodesics, which yields simple proofs of Dervan and Sektnan's uniqueness result for optimal symplectic connections and a boundedness result for the log-norm functional. Next, we associate to a fibration degeneration a unique geodesic ray defined on a dense open subset. Calculating the limiting slope of the log-norm functional along a globally defined smooth geodesic ray, we prove that fibrations admitting optimal symplectic connections are polystable with respect to a large class of fibration degenerations that are smooth over the base. We give examples of such degenerations in the case of projectivised vector bundles and isotrivial fibrations.
