Constructing a complete integral of the Hamilton-Jacobi equation on pseudo-Riemannian spaces with simply transitive groups of motions

2019/08/31 by A. A. Magazev · 1 citation
Physics and Astronomy · Mathematics · #math-ph #math.MP

paper · pdf · doi:10.1007/s11040-021-09385-3

published as Math Phys Anal Geom 24, 11 (2021) · 15 pages

arxiv created 2021/03/12 · arxiv updated 2021/03/25

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.

Cited by

• Classification of Einstein spaces with Stackel metric of type (3.0)