论文标题
在捆绑上处方标态曲率的直接方法
A direct approach to prescribing scalar curvature on bundles
论文作者
论文摘要
本说明旨在通过直接应用一些卡兹丹（Warner）结果来演示如何讨论标量曲率函数对捆绑包的可接受性。该概念的证据包括确定哪些功能可以实现为标量曲率函数，这是对异国歧管上几个束的总空间的标态函数。此外，我们采用传统的变分方法来提供合理的条件，以使某些纤维束的总空间平滑功能，以实现为某些Riemannian浸没指标的标态曲率函数。我们将这些最后的结果应用于calabi-yau歧管上的捆绑包。
This note intends to demonstrate how to discuss scalar curvature functions' admissibility on bundles by directly applying some of the Kazdan--Warner results. Proofs of the concept include determining which functions are realizable as scalar curvature functions on the total space of several bundles over exotic manifolds. In addition, we employ traditional variational methods to provide reasonable conditions to smooth functions on the total spaces of some fiber bundles to be realized as scalar curvature functions for some Riemannian submersions metrics. We apply these last results to bundles over Calabi--Yau manifolds.
