里奇平坦弦代数胚
Ricci-flat string algebroids
- Universidade Estadual de Campinas (UNICAMP)（坎皮纳斯州立大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文研究由4-形式定义的含挠率几何结构，构建统一框架导出弦代数胚，关联广义几何与杂化弦理论的规范结构，证明其诱导广义里奇平坦度量并构造显式例子。
AI中文摘要：
我们研究由4-形式定义的几何结构，涵盖带挠率的重要几何结构类，包括殆埃尔米特结构、$\text{G}_2$结构、$\text{Spin}(7)$结构以及殆四元数/超埃尔米特结构。在该统一框架内，基础4-形式自然确定定义流形上弦代数胚的几何数据，尤其产生规范的瞬子概念，从而将这些几何与广义几何及杂化弦理论中的规范理论结构关联起来。我们进一步证明这些数据诱导广义里奇平坦度量，最后考察文献中的主要例子并构造若干显式例子。
英文摘要：
We investigate geometric structures defined by 4-forms, encompassing important classes of geometric structures with torsion including almost Hermitian, $\mathrm{G}_2$, $\mathrm{Spin}(7)$, and almost quaternion/hyper Hermitian. Within this unified framework, the underlying 4-form naturally determines geometric data that define a string algebroid over the manifold. In particular, it gives rise to a canonical notion of instanton, thereby linking these geometries to gauge-theoretic structures in generalized geometry and heterotic string theory. We further prove that these data induce generalized Ricci-flat metrics. Finally, we examine the main examples in the literature and construct several explicit ones.
