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Sigma Models, Minimal Surfaces and Some Ricci Flat Pseudo Riemannian Geometries | | Metin Gurses
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9 Oct 2000 | | Subject: | Differential Geometry | math.DG | | Affiliation: | Bilkent University | | Abstract: | We consider the sigma models where the base metric is proportional to the metric of the configuration space. We show that the corresponding sigma model equation admits a Lax pair. We also show that this type of sigma models in two dimensions are intimately related to the minimal surfaces in a flat pseudo Riemannian 3-space. We define two dimensional surfaces conformally related to the minimal surfaces in flat three dimensional geometries which enable us to give a construction of the metrics of some even dimensional Ricci flat pseudo Riemannian geometries. | | Source: | arXiv, math.DG/0010081 | | Services: | Forum | Review | PDF | Favorites | |
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