Riemannian Manifolds with Diagonal Metric. The Lam\'e and Bourlet Systems
Abstract
We discuss a Lie algebraic and differential geometry construction of solutions to some multidimensional nonlinear integrable systems describing diagonal metrics on Riemannian manifolds, in particular those of zero and constant curvature. Here some special solutions to the Lam\'e and Bourlet type equations, determining by n arbitrary functions of one variable are obtained in an explicit form. For the case when the sum of the diagonal elements of the metric is a constant, these solutions are expressed as a product of the Jacobi elliptic functions and are determined by 2n arbitrary constants.
Cite
@article{arxiv.solv-int/9612004,
title = {Riemannian Manifolds with Diagonal Metric. The Lam\'e and Bourlet Systems},
author = {A. V. Razumov and M. V. Saveliev},
journal= {arXiv preprint arXiv:solv-int/9612004},
year = {2016}
}
Comments
LaTeX file, 22 pages, to appear in the proceedings of the international conference "Selected Topics of Theoretical and Modern Mathematical Physics (SIMI-96)", September 22-29, 1996, Tbilisi, Georgia