二维和三维大地线汉密尔顿-雅可比方程中的变量分离

IF 1 4区物理与天体物理 Q3 PHYSICS, MATHEMATICAL

Theoretical and Mathematical Physics Pub Date : 2024-02-27 DOI:10.1134/s0040577924020065

M. O. Katanaev

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引用次数: 0

摘要

摘要在二维和三维的（伪）黎曼流形上，我们列出了在汉密尔顿-雅可比方程中允许完全分离测地线变量的所有度量。二维曲面上有三类不同的可分离度量。三维流形有六类可分离度量。在每一类中，度量都通过典型变换和不依赖于坐标的参数非enerate 变换相关联。

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Separation of variables in the Hamilton–Jacobi equation for geodesics in two and three dimensions

Abstract

On (pseudo)Riemannian manifolds of two and three dimensions, we list all metrics that admit a complete separation of variables in the Hamilton–Jacobi equation for geodesics. There are three different classes of separable metrics on two-dimensional surfaces. Three-dimensional manifolds admit six classes of separable metrics. Within each class, metrics are related by canonical transformations and a nondegenerate transformation of parameters that does not depend on coordinates.

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来源期刊

Theoretical and Mathematical Physics 物理-物理：数学物理

CiteScore

1.60

自引率

20.00%

发文量

103

审稿时长

4-8 weeks

期刊介绍： Theoretical and Mathematical Physics covers quantum field theory and theory of elementary particles, fundamental problems of nuclear physics, many-body problems and statistical physics, nonrelativistic quantum mechanics, and basic problems of gravitation theory. Articles report on current developments in theoretical physics as well as related mathematical problems. Theoretical and Mathematical Physics is published in collaboration with the Steklov Mathematical Institute of the Russian Academy of Sciences.