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VOL. 2 | 2001 Sigma Models, Minimal Surfaces and Some Ricci Flat Pseudo-Riemannian Geometries


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.


Published: 1 January 2001
First available in Project Euclid: 5 June 2015

zbMATH: 1070.53503
MathSciNet: MR1815638

Digital Object Identifier: 10.7546/giq-2-2001-171-180

Rights: Copyright © 2001 Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences


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