论文标题
部分可观测时空混沌系统的无模型预测
A split special Lagrangian calibration associated with frame vorticity
论文作者
论文摘要
令M为定向的三维Riemannian歧管。我们定义了捆绑包的局部部分的涡度概念（m） - > m的所有正相向的正顺序切线框架。当m是空间形式时，我们将概念与iso_o（m）\ so（m）上合适的不变分式伪riemannian指标联系起来：当时局部部分具有正涡度，并且仅当它确定类似太空的亚曼福尔德时。在欧几里得的情况下，我们使用特殊的拉格朗日校准发现了明确的同源体积最大化部分。我们介绍了最佳框架涡度的概念，并为三个球员提供了最佳的全球部分。我们证明它也是同源量最大化（现在使用常见的单点拆分校准）。此外，我们表明欧几里得和双曲线病例中不存在最佳部分。
Let M be an oriented three-dimensional Riemannian manifold. We define a notion of vorticity of local sections of the bundle SO(M) --> M of all its positively oriented orthonormal tangent frames. When M is a space form, we relate the concept to a suitable invariant split pseudo-Riemannian metric on Iso_o (M) \cong SO(M): A local section has positive vorticity if and only if it determines a space-like submanifold. In the Euclidean case we find explicit homologically volume maximizing sections using a split special Lagrangian calibration. We introduce the concept of optimal frame vorticity and give an optimal screwed global section for the three-sphere. We prove that it is also homologically volume maximizing (now using a common one-point split calibration). Besides, we show that no optimal section can exist in the Euclidean and hyperbolic cases.
