dorsal/arxiv
View SchemaRiemannian Manifolds with Diagonal Metric. The Lam\'e and Bourlet Systems
| Authors | A. V. Razumov, M. V. Saveliev |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9612004 |
| URL | https://arxiv.org/abs/solv-int/9612004 |
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.
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"abstract": "We discuss a Lie algebraic and differential geometry construction of\nsolutions to some multidimensional nonlinear integrable systems describing\ndiagonal metrics on Riemannian manifolds, in particular those of zero and\nconstant curvature. Here some special solutions to the Lam\\\u0027e and Bourlet type\nequations, determining by n arbitrary functions of one variable are obtained in\nan explicit form. For the case when the sum of the diagonal elements of the\nmetric is a constant, these solutions are expressed as a product of the Jacobi\nelliptic functions and are determined by 2n arbitrary constants.",
"arxiv_id": "solv-int/9612004",
"authors": [
"A. V. Razumov",
"M. V. Saveliev"
],
"categories": [
"solv-int",
"dg-ga",
"hep-th",
"math.DG",
"nlin.SI"
],
"title": "Riemannian Manifolds with Diagonal Metric. The Lam\\\u0027e and Bourlet Systems",
"url": "https://arxiv.org/abs/solv-int/9612004"
},
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