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Teoreticheskaya i Matematicheskaya Fizika, 2024, Volume 218, Number 2, Pages 306–319
DOI: https://doi.org/10.4213/tmf10546 (Mi tmf10546) 		 
Separation of variables in the Hamilton–Jacobi equation for geodesics in two and three dimensions

M. O. Katanaevab

a Steklov Mathematical Institute, Russian Academy of Sciences, Moscow, Russia
b Lobachevsky Institute of Mathematics and Mechanics, Kazan (Volga Region) Federal University, Kazan, Russia
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DOI: https://doi.org/10.4213/tmf10546
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.
Keywords: Hamilton–Jacobi equation, separation of variables, geodesic.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation
This paper has been supported by the Kazan Federal University Strategic Academic Leadership.
Received: 29.05.2023
Revised: 21.06.2023
English version:
Theoretical and Mathematical Physics, 2024, Volume 218, Issue 2, Pages 264–275
DOI: https://doi.org/10.1134/S0040577924020065
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: M. O. Katanaev, “Separation of variables in the Hamilton–Jacobi equation for geodesics in two and three dimensions”, TMF, 218:2 (2024), 306–319; Theoret. and Math. Phys., 218:2 (2024), 264–275
Citation in format AMSBIB
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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