AI 中文总结
本文研究常曲率二维空间（球面、罗氏空间）上的Bertrand系统，采用基于Laplace-Beltrami算子的量子化技术处理经典模型，分析其量子行为。
AI 中文摘要
本文讨论常曲率二维空间即球面和伪球面（罗氏空间）上的Bertrand系统，该类模型常采用基于Laplace-Beltrami算子的量子化技术作用于经典模型，并分析所得量子行为。
英文摘要
Discussed are Bertrand systems on two-dimensional spaces of constant curvature, i.e. sphere and pseudosphere (Lobachevsky space). These models often involve applying quantization techniques, such as those based on the Laplace-Beltrami operator, to the classical models and analyzing the resulting quantum behavior.
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