交比几何
Geometry of cross ratio
摘要：
推广的交比极化的线性有限和无限维空间（特别是佐藤格拉斯曼）给出和探讨。这交比似乎是一个上循环的规范（互逻辑）丛在格拉斯曼与系数层的自同态。定义了Schwarz微分的算子模拟。建立了它与线性哈密顿系统和Riccati方程的联系。这些构造的目的是获得KP-层次的应用。
英文摘要：
Generalization of the cross ratio to polarizations of linear finite and infinite-dimensional spaces (in particular to Sato Grassmannian) is given and explored. This cross ratio appears to be a cocycle of the canonical (tautalogical) bundle over the Grassmannian with coefficients in the sheaf of its endomorphisms. Operator analog of the Schwarz differential is defined. Its connections to linear Hamiltonian systems and Riccati equations are established. These constructions aim to obtain applications to KP-hierarchy.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
