A system of PDEs for Riemannian spaces

• Autores: Padma Senarath, Gillian Thornley, Bruce van Brunt
• Localización: Journal of the Australian Mathematical Society, ISSN 1446-7887, Vol. 82, Nº 2, 2007, págs. 249-262
• Idioma: inglés
• DOI: 10.1017/s1446788700016062
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• Resumen

  • Matsumoto [10] remarked that some locally projectively flat Finsler spaces of non-zero constant curvature may be Riemannian spaces of non-zero constant curvature. The Riemannian connection, however, must be metric compatible, and this requirement places restrictions on the geodesic coefficients for the Finsler space in the form of a system of partial differential equations. In this paper, we derive this system of equations for the case where the geodesic coefficients are quadratic in the tangent space variables y2, and determine the solutions. We recover two standard Riemannian metrics of non-zero constant curvature from this class of solutions.