论文标题
类型IIA字符串的几何流动
Geometric Flows for the Type IIA String
论文作者
论文摘要
引入了$ 6 $维符号歧管上的几何流量，这是由IIA型字符串的超对称压缩动机的。底层结构被证明是SU（3）载体，但就几乎温和的结构的李维维 - 基维塔连接而言。建立了短时的存在，发现Nijenhuis张量的新身份对于Shi-Type估计至关重要。可以完全解决该集成的情况，从而为Yau定理提供了有关Ricci-FlatKähler指标的替代证明。在不可综合的情况下，制定了模型，这表明该流量应导致与给定符号形式兼容的最佳几乎复合结构。
A geometric flow on $6$-dimensional symplectic manifolds is introduced which is motivated by supersymmetric compactifications of the Type IIA string. The underlying structure turns out to be SU(3) holonomy, but with respect to the projected Levi-Civita connection of an almost-Hermitian structure. The short-time existence is established, and new identities for the Nijenhuis tensor are found which are crucial for Shi-type estimates. The integrable case can be completely solved, giving an alternative proof of Yau's theorem on Ricci-flat Kähler metrics. In the non-integrable case, models are worked out which suggest that the flow should lead to optimal almost-complex structures compatible with the given symplectic form.
