Abstract
In this work, an efficient method for constructing a complete integral of the geodesic Hamilton–Jacobi equation on pseudo-Riemannian manifolds with simply transitive groups of motions is suggested. The method is based on using a special transition to canonical coordinates on coadjoint orbits of the group of motion. As a non-trivial example, we consider the problem of constructing a complete integral of the geodesic Hamilton–Jacobi equation in the McLenaghan–Tariq–Tupper spacetime. An essential feature of this example is that the Hamilton-Jacobi equation is not separable in the corresponding configuration space.
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Acknowledgements
The author expresses his deep gratitude to Igor V. Shirokov for his constant and fruitful discussions and support. Dr. S. V. Danilova is gratefully acknowledged for careful reading of the manuscript.
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Magazev, A.A. Constructing a Complete Integral of the Hamilton–Jacobi Equation on Pseudo-Riemannian Spaces with Simply Transitive Groups of Motions. Math Phys Anal Geom 24, 11 (2021). https://doi.org/10.1007/s11040-021-09385-3
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DOI: https://doi.org/10.1007/s11040-021-09385-3
Keywords
- Geodesic Hamilton–Jacobi equation
- Simply transitive action
- Lie group
- Coadjoint orbit
- Darboux coordinates