Proceedings of the International Conference on Geometry, Integrability and Quantization

Sigma Models, Minimal Surfaces and Some Ricci Flat Pseudo-Riemannian Geometries

Metin Gürses

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.

Article information

Source
Proceedings of the Second International Conference on Geometry, Integrability and Quantization, Ivaïlo M. Mladenov and Gregory L. Naber, eds. (Sofia: Coral Press Scientific Publishing, 2001), 171-180

Dates
First available in Project Euclid: 5 June 2015

Permanent link to this document
https://projecteuclid.org/ euclid.pgiq/1433528472

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

Mathematical Reviews number (MathSciNet)
MR1815638

Zentralblatt MATH identifier
1070.53503

Citation

Gürses, Metin. Sigma Models, Minimal Surfaces and Some Ricci Flat Pseudo-Riemannian Geometries. Proceedings of the Second International Conference on Geometry, Integrability and Quantization, 171--180, Coral Press Scientific Publishing, Sofia, Bulgaria, 2001. doi:10.7546/giq-2-2001-171-180. https://projecteuclid.org/euclid.pgiq/1433528472


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