二阶超可积系统与Weyl几何
Second-order superintegrable systems and Weylian geometry
AI总结：
本文通过揭示二阶最大共形超可积哈密顿系统背后的自然Weyl结构，将共形超可积性概念推广到Weyl几何，并将其解释为与统计流形和仿射超曲面理论相关的半Weyl结构。
摘要：
本文重新考察了大量二阶最大共形超可积哈密顿系统，揭示了它们潜在的自然Weyl结构，并为Stäckel变换（也称为耦合常数变形）的研究提供了更清晰的几何背景。这也使我们能够将共形超可积性的概念从共形几何领域自然地推广到Weyl结构领域。它使我们能够将上述类型的超可积系统解释为半Weyl结构，这一概念与统计流形和仿射超曲面理论相关。
英文摘要：
Abundant second-order maximally conformally superintegrable Hamiltonian systems are re-examined, revealing their underlying natural Weyl structure and offering a clearer geometric context for the study of Stäckel transformations (also known as coupling constant metamorphosis). This also allows us to naturally extend the concept of conformal superintegrability from the realm of conformal geometries to that of Weyl structures. It enables us to interpret superintegrable systems of the above type as semi-Weyl structures, a concept related to statistical manifolds and affine hypersurface theory.
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。
