Moduli spaces for finite-order jets of Riemannian metrics

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Moduli spaces for finite-order jets of Riemannian metrics

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Title: Moduli spaces for finite-order jets of Riemannian metrics
Author: Gordillo Merino, Adrián; Navarro Garmendia, José; Sancho de Salas, Juan Bautista
Abstract: Construimos el espacio de módulos de r-jets en un punto de la métrica de Riemann sobre un colector fluido. La construcción está estrechamente relacionado con el problema de la clasificación de las métricas de chorro a través de invariantes diferenciales. El espacio de módulos se prueba para ser un espacio diferenciable que admite una estratificación canónica finita en colectores fluidos. Un estudio completo sobre la estratificación de espacios modulares se lleva a cabo para las métricas de dimensión n=2.We construct the moduli space of r−jets of Riemannian metrics at a point on a smooth manifold. The construction is closely related to the problem of classification of jet metrics via differential invariants. The moduli space is proved to be a differentiable space which admits a finite canonical stratification into smooth manifolds. A complete study on the stratification of moduli spaces is carried out for metrics in dimension n=2.
Description: Publicado en: Differential Geometry and its Applications, Volume 28, Issue 6, Dec 2010, pages 672-688 DOI: 10.1016/j.difgeo.2010.07.002
URI: http://hdl.handle.net/10662/2563
Date: 2009-03


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