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Riemannian Manifolds with Diagonal Metric. The Lam\'e and Bourlet Systems by Razumov, A. V.; Saveliev, M. V. is a scholarly article available to read on EtoBox.

What is Riemannian Manifolds with Diagonal Metric. The Lam\'e and Bourlet Systems about?

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.

Author

Razumov, A. V.; Saveliev, M. V.

Published

1996

Language

EN